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Mathematics Subject Classification – Geometry

GEOMETRY

AMS: 51       All of this section
AMS: 51-XX    Not classified at a more specific level

• AMS: 51-00    General reference works
• AMS: 51-01    Instructional exposition
• AMS: 51-02    Research exposition
• AMS: 51-03    Historical
• AMS: 51-04    Explicit machine computation and programs
• AMS: 51-06    Proceedings, conferences, collections, etc.

• AMS: 51Axx    Linear incidence geometry
  AMS: 51A*     (including sub-levels)
  • AMS: 51A05    General theory and projective geometries
  • AMS: 51A10    Homomorphism, automorphism and dualities
  • AMS: 51A25    Algebraization
  • AMS: 51A40    Translation planes and spreads
  • AMS: 51A45    Incidence structures imbeddable into projective geometries
  • AMS: 51A99    None of the above, but in this section
• AMS: 51Bxx    Nonlinear incidence geometry
  AMS: 51B*     (including sub-levels)
  • AMS: 51B10    Möbius geometries
• AMS: 51Cxx    Ring geometry (Hjelmslev, Barbilian, etc.)
  AMS: 51C*     (including sub-levels)
  • AMS: 51C05    Ring geometry (Hjelmslev, Barbilian, etc.)
• AMS: 51Dxx    Geometric closure systems
  AMS: 51D*     (including sub-levels)
  • AMS: 51D20    Combinatorial geometries
• AMS: 51Exx    Finite geometry and special incidence structures
  AMS: 51E*     (including sub-levels)
  • AMS: 51E05    General block designs
  • AMS: 51E10    Steiner systems
  • AMS: 51E12    Generalized quadrangles, generalized polygons
  • AMS: 51E14    Finite partial geometries (general), nets, partial spreads
  • AMS: 51E15    Affine and projective planes
  • AMS: 51E20    Combinatorial structures in finite projective spaces
  • AMS: 51E22    Linear codes and caps in Galois spaces
  • AMS: 51E24    Buildings and the geometry of diagrams
  • AMS: 51E25    Other finite nonlinear geometries
  • AMS: 51E30    Other finite incidence structures
• AMS: 51Fxx    Metric geometry
  AMS: 51F*     (including sub-levels)
  • AMS: 51F05    Absolute planes
  • AMS: 51F15    Reflection groups, reflection geometries
  • AMS: 51F20    Congruence and orthogonality
• AMS: 51Gxx    Ordered geometries (ordered incidence structures, etc.)
  AMS: 51G*     (including sub-levels)
  • AMS: 51G05    Ordered geometries (ordered incidence structures, etc.)
• AMS: 51Hxx    Topological geometry
  AMS: 51H*     (including sub-levels)
  • AMS: 51H10    Topological linear incidence structures
  • AMS: 51h20    Topological geometries on manifolds
  • AMS: 51h25    Geometries with differentiable structure
  • AMS: 51H99    None of the above, but in this section
• AMS: 51Jxx    Incidence groups
  AMS: 51J*     (including sub-levels)
• AMS: 51Kxx    Distance geometry
  AMS: 51K*     (including sub-levels)
• AMS: 51Lxx    Geometric order structures
  AMS: 51L*     (including sub-levels)
• AMS: 51Mxx    Real and complex geometry
  AMS: 51M*     (including sub-levels)
  • AMS: 51M04    Elementary problems in Euclidean geometries
  • AMS: 51M05    Euclidean geometries (general) and generalizations
  • AMS: 51M09    Elementary problems in hyperbolic and elliptic geometries
  • AMS: 51M10    Hyperbolic and elliptic geometries (general) and generalizations
  • AMS: 51M15    Geometric constructions
  • AMS: 51M16    Inequalities and extremum problems
  • AMS: 51M20    Polyhedra and polytopes; regular figures, division of spaces
  • AMS: 51M25    Length, area and volume
  • AMS: 51M30    Line geometries and their generalizations
  • AMS: 51M35    Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)
  • AMS: 51M99    None of the above, but in this section
• AMS: 51Nxx    Analytic and descriptive geometry
  AMS: 51N*     (including sub-levels)
  • AMS: 51N05    Descriptive geometry
  • AMS: 51N10    Affine analytic geometry
  • AMS: 51N15    Projective analytic geometry
  • AMS: 51N20    Euclidean analytic geometry
  • AMS: 51N30    Geometry of classical groups
  • AMS: 51N35    Questions of classical algebraic geometry
  • AMS: 51N99    None of the above, but in this section
• AMS: 51Pxx    Geometry and physics
  AMS: 51P*     (including sub-levels)
  • AMS: 51P05    Geometry and physics

CONVEX AND DISCRETE GEOMETRY

AMS: 52       All of this section
AMS: 52-XX    Not classified at a more specific level

• AMS: 52-00    General reference works
• AMS: 52-01    Instructional exposition
• AMS: 52-02    Research exposition
• AMS: 52-03    Historical
• AMS: 52-06    Proceedings, conferences, collections, etc.

• AMS: 52Axx    General convexity
  AMS: 52A*     (including sub-levels)
  • AMS: 52A05    Convex sets without dimension restrictions
  • AMS: 52A07    Convex sets in topological vector spaces
  • AMS: 52A10    Convex sets in $2$ dimensions (including convex curves)
  • AMS: 52A15    Convex sets in $3$ dimensions (including convex surfaces)
  • AMS: 52A20    Convex sets in $n$ dimensions (including convex hypersurfaces)
  • AMS: 52A22    Random convex sets and integral geometry
  • AMS: 52A30    Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)
  • AMS: 52A35    Helly-type theorems and geometric transversal theory
  • AMS: 52A37    Other problems of combinatorial convexity
  • AMS: 52A40    Inequalities and extremum problems
  • AMS: 52A41    Convex functions and convex programs
  • AMS: 52A99    None of the above, but in this section
• AMS: 52Bxx    Polytopes and polyhedra
  AMS: 52B*     (including sub-levels)
  • AMS: 52B05    Combinatorial properties (number of faces, shortest paths, etc.)
  • AMS: 52B11    $n$-dimensional polytopes
  • AMS: 52B12    Special polytopes (linear programming, centrally symmetric, etc.)
  • AMS: 52B15    Symmetry properties of polytopes
  • AMS: 52B20    Lattice polytopes (including relations with commutative algebra and algebraic geometry)
  • AMS: 52B40    Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
  • AMS: 52B55    Computational aspects related to convexity
  • AMS: 52B99    None of the above, but in this section
• AMS: 52Cxx    Discrete geometry
  AMS: 52C*     (including sub-levels)
  • AMS: 52C05    Lattices and convex bodies in $2$ dimensions
  • AMS: 52C07    Lattices and convex bodies in $n$ dimensions
  • AMS: 52C15    Packing and covering in $2$ dimensions
  • AMS: 52C17    Packing and covering in $n$ dimensions
  • AMS: 52C20    Tilings in $2$ dimensions
  • AMS: 52C22    Tilings in $n$ dimensions
  • AMS: 52C25    Rigidity and flexibility of structures
  • AMS: 52C35    Arrangements of points, flats, hyperplanes

DIFFERENTIAL GEOMETRY

AMS: 53       All of this section
AMS: 53-XX    Not classified at a more specific level

• AMS: 53-00    General reference works
• AMS: 53-01    Instructional exposition
• AMS: 53-02    Research exposition
• AMS: 53-03    Historical
• AMS: 53-06    Proceedings, conferences, collections, etc.

• AMS: 53Axx    Classical differential geometry
  AMS: 53A*     (including sub-levels)
  • AMS: 53A04    Curves in Euclidean space
  • AMS: 53A05    Surfaces in Euclidean space
  • AMS: 53A07    Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
  • AMS: 53A10    Minimal surfaces, surfaces with prescribed mean curvature
  • AMS: 53A15    Affine differential geometry
  • AMS: 53A17    Kinematics
  • AMS: 53A20    Projective differential geometry
  • AMS: 53A25    Differential line geometry
  • AMS: 53A30    Conformal differential geometry
  • AMS: 53A35    Non-Euclidean differential geometry
  • AMS: 53A40    Other special differential geometries
  • AMS: 53A45    Vector and tensor analysis
  • AMS: 53A55    Differential invariants (local theory), geometric objects
• AMS: 53Bxx    Local differential geometry
  AMS: 53B*     (including sub-levels)
  • AMS: 53B05    Linear and affine connections
  • AMS: 53B15    Other connections
  • AMS: 53B20    Local Riemannian geometry
  • AMS: 53B21    Methods of Riemannian geometry
  • AMS: 53B25    Local submanifolds
  • AMS: 53B30    Lorentz metrics, indefinite metrics
  • AMS: 53B35    Hermitian and Kählerian structures
  • AMS: 53B40    Finsler spaces and generalizations (areal metrics)
  • AMS: 53B50    Applications to physics
  • AMS: 53B99    None of the above, but in this section
• AMS: 53Cxx    Global differential geometry
  AMS: 53C*     (including sub-levels)
  • AMS: 53C05    Connections, general theory
  • AMS: 53C07    Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
  • AMS: 53C10    $G$-structures
  • AMS: 53C12    Foliations (differential geometric aspects)
  • AMS: 53C15    General geometric structures on manifolds (almost complex, almost product structures, etc.)
  • AMS: 53C17    Sub-Riemannian geometry
  • AMS: 53C20    Global Riemannian geometry, including pinching
  • AMS: 53C21    Methods of Riemannian geometry, including PDE methods; curvature restrictions
  • AMS: 53C22    Geodesics
  • AMS: 53C23    Global topological methods (à la Gromov)
  • AMS: 53C24    Rigidity results
  • AMS: 53C25    Special Riemannian manifolds (Einstein, Sasakian, etc.)
  • AMS: 53C26    Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry
  • AMS: 53C27    Spin and Spin$^c$ geometry
  • AMS: 53C28    Twistor methods
  • AMS: 53C29    Issues of holonomy
  • AMS: 53C30    Homogeneous manifolds
  • AMS: 53C35    Symmetric spaces
  • AMS: 53C40    Global submanifolds
  • AMS: 53C42    Immersions (minimal, prescribed curvature, tight, etc.)
  • AMS: 53C43    Differential geometric aspects of harmonic maps
  • AMS: 53C44    Geometric evolution equations (mean curvature flow)
  • AMS: 53C45    Global surface theory (convex surfaces à la A. D. Aleksandrov)
  • AMS: 53C50    Lorentz manifolds, manifolds with indefinite metrics
  • AMS: 53C55    Hermitian and Kählerian manifolds
  • AMS: 53C56    Other complex differential geometry
  • AMS: 53C60    Finsler spaces and generalizations (areal metrics)
  • AMS: 53C65    Integral geometry
  • AMS: 53C70    Direct methods ($G$-spaces of Busemann, etc.)
  • AMS: 53C80    Applications to physics
  • AMS: 53C99    None of the above, but in this section
• AMS: 53Dxx    Symplectic geometry, contact geometry
  AMS: 53D*     (including sub-levels)
  • AMS: 53D05    Symplectic manifolds, general
  • AMS: 53D12    Lagrangian submanifolds; Maslov index
  • AMS: 53D15    Almost contact and almost symplectic manifolds
  • AMS: 53D17    Poisson manifolds
  • AMS: 53D20    Momentum maps; symplectic reduction
  • AMS: 53D25    Geodesic flows
  • AMS: 53D35    Global theory of symplectic and contact manifolds
  • AMS: 53D40    Floer homology and cohomology, symplectic aspects
  • AMS: 53D45    Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
  • AMS: 53D50    Geometric quantization
  • AMS: 53D55    Deformation quantization, star products
  • AMS: 53D99    None of the above, but in this section
• AMS: 53Zxx    Applications to physics
  AMS: 53Z*     (including sub-levels)
  • AMS: 53Z05    Applications to physics

GENERAL TOPOLOGY

AMS: 54       All of this section
AMS: 54-XX    Not classified at a more specific level

• AMS: 54-01    Instructional exposition
• AMS: 54-02    Research exposition
• AMS: 54-03    Historical
• AMS: 54-06    Proceedings, conferences, collections, etc.

• AMS: 54Axx    Generalities
  AMS: 54A*     (including sub-levels)
  • AMS: 54A05    Topological spaces and generalizations (closure spaces, etc.)
  • AMS: 54A10    Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
  • AMS: 54A20    Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
  • AMS: 54A25    Cardinality properties (cardinal functions and inequalities, discrete subsets)
• AMS: 54Bxx    Basic constructions
  AMS: 54B*     (including sub-levels)
  • AMS: 54B15    Quotient spaces, decompositions
  • AMS: 54B20    Hyperspaces
  • AMS: 54B30    Categorical methods
  • AMS: 54B40    Presheaves and sheaves
• AMS: 54Cxx    Maps and general types of spaces defined by maps
  AMS: 54C*     (including sub-levels)
  • AMS: 54C15    Retraction
  • AMS: 54C20    Extension of maps
  • AMS: 54C25    Embedding
  • AMS: 54C30    Real-valued functions
  • AMS: 54C40    Algebraic properties of function spaces
  • AMS: 54C50    Special sets defined by functions
  • AMS: 54C55    Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
  • AMS: 54C56    Shape theory
  • AMS: 54C60    Set-valued maps
  • AMS: 54C65    Selections
  • AMS: 54C70    Entropy
• AMS: 54Dxx    Fairly general properties
  AMS: 54D*     (including sub-levels)
  • AMS: 54D05    Connected and locally connected spaces (general aspects)
  • AMS: 54D15    Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
  • AMS: 54D20    Noncompact covering properties (paracompact, Lindelöf, etc.)
  • AMS: 54D45    Local compactness, $\sigma$-compactness
  • AMS: 54D50    $k$-spaces
  • AMS: 54D99    None of the above, but in this section
• AMS: 54Exx    Spaces with richer structures
  AMS: 54E*     (including sub-levels)
  • AMS: 54E15    Uniform structures and generalizations
  • AMS: 54E18    $p$-spaces, $M$-spaces, $\sigma$-spaces, etc.
  • AMS: 54E25    Semimetric spaces
  • AMS: 54E30    Moore spaces
  • AMS: 54E35    Metric spaces, metrizability
  • AMS: 54E40    Special maps on metric spaces
  • AMS: 54E50    Complete metric spaces
  • AMS: 54E99    None of the above, but in this section
• AMS: 54Fxx    Special properties
  AMS: 54F*     (including sub-levels)
  • AMS: 54F05    Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
  • AMS: 54F15    Continua and generalizations
  • AMS: 54F35    Higher-dimensional local connectedness
  • AMS: 54F45    Dimension theory
  • AMS: 54F50    Spaces of dimension $\leq 1$; curves, dendrites
  • AMS: 54F65    Topological characterizations of particular spaces
• AMS: 54Gxx    Peculiar spaces
  AMS: 54G*     (including sub-levels)
• AMS: 54Hxx    Connections with other structures, applications
  AMS: 54H*     (including sub-levels)
  • AMS: 54H05    Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
  • AMS: 54H12    Topological lattices, etc.
  • AMS: 54H15    Transformation groups and semigroups
  • AMS: 54h20    Topological dynamics
  • AMS: 54h25    Fixed-point and coincidence theorems
• AMS: 54Jxx    Nonstandard topology
  AMS: 54J*     (including sub-levels)
  • AMS: 54J05    Nonstandard topology

ALGEBRAIC TOPOLOGY

AMS: 55       All of this section
AMS: 55-XX    Not classified at a more specific level

• AMS: 55-00    General reference works
• AMS: 55-01    Instructional exposition
• AMS: 55-02    Research exposition
• AMS: 55-03    Historical
• AMS: 55-04    Explicit machine computation and programs
• AMS: 55-06    Proceedings, conferences, collections, etc.

• AMS: 55Mxx    Classical topics
  AMS: 55M*     (including sub-levels)
  • AMS: 55M05    Duality
  • AMS: 55M15    Absolute neighborhood retracts
  • AMS: 55M20    Fixed points and coincidences
  • AMS: 55M25    Degree, winding number
  • AMS: 55M30    Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
  • AMS: 55M35    Finite groups of transformations (including Smith theory)
• AMS: 55Nxx    Homology and cohomology theories
  AMS: 55N*     (including sub-levels)
  • AMS: 55N07    Steenrod-Sitnikov homologies
  • AMS: 55N10    Singular theory
  • AMS: 55N15    $K$-theory
  • AMS: 55N20    Generalized (extraordinary) homology and cohomology theories
  • AMS: 55N22    Bordism and cobordism theories, formal group laws
  • AMS: 55N25    Homology with local coefficients, equivariant cohomology
  • AMS: 55N30    Sheaf cohomology
  • AMS: 55N33    Intersection homology and cohomology
  • AMS: 55N35    Other homology theories
  • AMS: 55N40    Axioms for homology theory and uniqueness theorems
  • AMS: 55N45    Products and intersections
  • AMS: 55N91    Equivariant homology and cohomology
  • AMS: 55N99    None of the above, but in this section
• AMS: 55Pxx    Homotopy theory
  AMS: 55P*     (including sub-levels)
  • AMS: 55P10    Homotopy equivalences
  • AMS: 55P15    Classification of homotopy type
  • AMS: 55P20    Eilenberg-Mac Lane spaces
  • AMS: 55P25    Spanier-Whitehead duality
  • AMS: 55P30    Eckmann-Hilton duality
  • AMS: 55P35    Loop spaces
  • AMS: 55P42    Stable homotopy theory, spectra
  • AMS: 55P45    $H$-spaces and duals
  • AMS: 55P47    Infinite loop spaces
  • AMS: 55P48    Loop space machines, operads
  • AMS: 55P50    String topology
  • AMS: 55P57    Proper homotopy theory
  • AMS: 55P60    Localization and completion
  • AMS: 55P62    Rational homotopy theory
  • AMS: 55P91    Equivariant homotopy theory
  • AMS: 55P92    Relations between equivariant and nonequivariant homotopy theory
  • AMS: 55P99    None of the above, but in this section
• AMS: 55Qxx    Homotopy groups
  AMS: 55Q*     (including sub-levels)
  • AMS: 55Q10    Stable homotopy groups
  • AMS: 55Q25    Hopf invariants
  • AMS: 55Q40    Homotopy groups of spheres
  • AMS: 55Q45    Stable homotopy of spheres
  • AMS: 55Q50    $J$-morphism
  • AMS: 55Q52    Homotopy groups of special spaces
  • AMS: 55Q91    Equivariant homotopy groups
• AMS: 55Rxx    Fiber spaces and bundles
  AMS: 55R*     (including sub-levels)
  • AMS: 55R05    Fiber spaces
  • AMS: 55R10    Fiber bundles
  • AMS: 55R12    Transfer
  • AMS: 55R15    Classification
  • AMS: 55R20    Spectral sequences and homology of fiber spaces
  • AMS: 55R25    Sphere bundles and vector bundles
  • AMS: 55R35    Classifying spaces of groups and $H$-spaces
  • AMS: 55R40    Homology of classifying spaces, characteristic classes
  • AMS: 55R50    Stable classes of vector space bundles, $K$-theory
  • AMS: 55R65    Generalizations of fiber spaces and bundles
  • AMS: 55R70    Fibrewise topology
  • AMS: 55R80    Discriminantal varieties, configuration spaces
  • AMS: 55R91    Equivariant fiber spaces and bundles
  • AMS: 55R99    None of the above, but in this section
• AMS: 55Sxx    Operations and obstructions
  AMS: 55S*     (including sub-levels)
  • AMS: 55S05    Primary cohomology operations
  • AMS: 55S10    Steenrod algebra
  • AMS: 55S25    $K$-theory operations and generalized cohomology operations
  • AMS: 55S30    Massey products
  • AMS: 55S35    Obstruction theory
  • AMS: 55S36    Extension and compression of mappings
  • AMS: 55S45    Postnikov systems, $k$-invariants
  • AMS: 55S91    Equivariant operations and obstructions
• AMS: 55Txx    Spectral sequences
  AMS: 55T*     (including sub-levels)
  • AMS: 55T10    Serre spectral sequences
  • AMS: 55T15    Adams spectral sequences
  • AMS: 55T20    Eilenberg-Moore spectral sequences
  • AMS: 55T25    Generalized cohomology
  • AMS: 55T99    None of the above, but in this section
• AMS: 55Uxx    Applied homological algebra and category theory
  AMS: 55U*     (including sub-levels)
  • AMS: 55U05    Abstract complexes
  • AMS: 55U10    Simplicial sets and complexes
  • AMS: 55U35    Abstract and axiomatic homotopy theory
  • AMS: 55U40    Topological categories, foundations of homotopy theory
  • AMS: 55U99    None of the above, but in this section

MANIFOLDS AND CELL COMPLEXES

AMS: 57       All of this section
AMS: 57-XX    Not classified at a more specific level

• AMS: 57-00    General reference works
• AMS: 57-01    Instructional exposition
• AMS: 57-02    Research exposition
• AMS: 57-03    Historical
• AMS: 57-06    Proceedings, conferences, collections, etc.

• AMS: 57Mxx    Low-dimensional topology
  AMS: 57M*     (including sub-levels)
  • AMS: 57M05    Fundamental group, presentations, free differential calculus
  • AMS: 57M07    Topological methods in group theory
  • AMS: 57M10    Covering spaces
  • AMS: 57M12    Special coverings, e.g. branched
  • AMS: 57M15    Relations with graph theory
  • AMS: 57M20    Two-dimensional complexes
  • AMS: 57M25    Knots and links in $S^3$
  • AMS: 57M27    Invariants of knots and 3-manifolds
  • AMS: 57M30    Wild knots and surfaces, etc., wild embeddings
  • AMS: 57M40    Characterizations of $E^3$ and $S^3$ (Poincaré conjecture)
  • AMS: 57M50    Geometric structures on low-dimensional manifolds
  • AMS: 57M60    Group actions in low dimensions
  • AMS: 57M99    None of the above, but in this section
• AMS: 57Nxx    Topological manifolds
  AMS: 57N*     (including sub-levels)
  • AMS: 57N05    Topology of $E^2$, $2$-manifolds
  • AMS: 57N10    Topology of general $3$-manifolds
  • AMS: 57N12    Topology of $E^3$ and $S^3$
  • AMS: 57N13    Topology of $E^4$, $4$-manifolds
  • AMS: 57N15    Topology of $E^n$, $n$-manifolds ($4 < n < \infty$)
  • AMS: 57N16    Geometric structures on manifolds
  • AMS: 57N20    Topology of infinite-dimensional manifolds
  • AMS: 57N60    Cellularity
  • AMS: 57N65    Algebraic topology of manifolds
  • AMS: 57N70    Cobordism and concordance
• AMS: 57Pxx    Generalized manifolds
  AMS: 57P*     (including sub-levels)
  • AMS: 57P05    Local properties of generalized manifolds
  • AMS: 57P10    Poincaré duality spaces
• AMS: 57Qxx    PL-topology
  AMS: 57Q*     (including sub-levels)
  • AMS: 57Q05    General topology of complexes
  • AMS: 57Q10    Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
  • AMS: 57Q12    Wall finiteness obstruction for CW-complexes
  • AMS: 57Q20    Cobordism
  • AMS: 57Q45    Knots and links (in high dimensions)
  • AMS: 57Q55    Approximations
• AMS: 57Rxx    Differential topology
  AMS: 57R*     (including sub-levels)
  • AMS: 57R05    Triangulating
  • AMS: 57R10    Smoothing
  • AMS: 57R12    Smooth approximations
  • AMS: 57R15    Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
  • AMS: 57R17    Symplectic and contact topology
  • AMS: 57R19    Algebraic topology on manifolds
  • AMS: 57R20    Characteristic classes and numbers
  • AMS: 57R22    Topology of vector bundles and fiber bundles
  • AMS: 57R25    Vector fields, frame fields
  • AMS: 57R27    Controllability of vector fields on $C^\infty$ and real-analytic manifolds
  • AMS: 57R30    Foliations; geometric theory
  • AMS: 57R32    Classifying spaces for foliations; Gelfand-Fuks cohomology
  • AMS: 57R35    Differentiable mappings
  • AMS: 57R40    Embeddings
  • AMS: 57R42    Immersions
  • AMS: 57R45    Singularities of differentiable mappings
  • AMS: 57R55    Differentiable structures
  • AMS: 57R56    Topological quantum field theories
  • AMS: 57R57    Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants
  • AMS: 57R65    Surgery and handlebodies
  • AMS: 57R67    Surgery obstructions, Wall groups
  • AMS: 57R70    Critical points and critical submanifolds
  • AMS: 57R75    O- and SO-cobordism
  • AMS: 57R77    Complex cobordism (U- and SU-cobordism)
  • AMS: 57R80    $h$- and $s$-cobordism
  • AMS: 57R85    Equivariant cobordism
  • AMS: 57R90    Other types of cobordism
  • AMS: 57R91    Equivariant algebraic topology of manifolds
  • AMS: 57R99    None of the above, but in this section
• AMS: 57Sxx    Topological transformation groups
  AMS: 57S*     (including sub-levels)
  • AMS: 57S05    Topological properties of groups of homeomorphisms or diffeomorphisms
  • AMS: 57S10    Compact groups of homeomorphisms
  • AMS: 57S15    Compact Lie groups of differentiable transformations
  • AMS: 57S17    Finite transformation groups
  • AMS: 57S20    Noncompact Lie groups of transformations
  • AMS: 57S25    Groups acting on specific manifolds
  • AMS: 57S30    Discontinuous groups of transformations
• AMS: 57Txx    Homology and homotopy of topological groups and related structures
  AMS: 57T*     (including sub-levels)
  • AMS: 57T05    Hopf algebras
  • AMS: 57T15    Homology and cohomology of homogeneous spaces of Lie groups
  • AMS: 57T25    Homology and cohomology of $H$-spaces
  • AMS: 57T30    Bar and cobar constructions
  • AMS: 57T35    Applications of Eilenberg-Moore spectral sequences

GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS

AMS: 58       All of this section
AMS: 58-XX    Not classified at a more specific level

• AMS: 58-01    Instructional exposition
• AMS: 58-02    Research exposition
• AMS: 58-03    Historical
• AMS: 58-06    Proceedings, conferences, collections, etc.

• AMS: 58Axx    General theory of differentiable manifolds
  AMS: 58A*     (including sub-levels)
  • AMS: 58A05    Differentiable manifolds, foundations
  • AMS: 58A07    Real-analytic and Nash manifolds
  • AMS: 58A10    Differential forms
  • AMS: 58A12    de Rham theory
  • AMS: 58A14    Hodge theory
  • AMS: 58A15    Exterior differential systems (Cartan theory)
  • AMS: 58A17    Pfaffian systems
  • AMS: 58A20    Jets
  • AMS: 58A25    Currents
  • AMS: 58A35    Stratified sets
  • AMS: 58A50    Supermanifolds and graded manifolds
• AMS: 58Bxx    Infinite-dimensional manifolds
  AMS: 58B*     (including sub-levels)
  • AMS: 58B05    Homotopy and topological questions
  • AMS: 58B10    Differentiability questions
  • AMS: 58B20    Riemannian, Finsler and other geometric structures
  • AMS: 58B25    Group structures and generalizations on infinite-dimensional manifolds
  • AMS: 58B32    Geometry of quantum groups
  • AMS: 58B34    Noncommutative geometry (à la Connes)
  • AMS: 58B99    None of the above, but in this section
• AMS: 58Cxx    Calculus on manifolds; nonlinear operators
  AMS: 58C*     (including sub-levels)
  • AMS: 58C06    Set valued and function-space valued mappings
  • AMS: 58C20    Differentiation theory (Gateaux, Fréchet, etc.)
  • AMS: 58C25    Differentiable maps
  • AMS: 58C30    Fixed point theorems on manifolds
  • AMS: 58C35    Integration on manifolds; measures on manifolds
  • AMS: 58C40    Spectral theory; eigenvalue problems
  • AMS: 58C50    Analysis on supermanifolds or graded manifolds
  • AMS: 58C99    None of the above, but in this section
• AMS: 58Dxx    Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
  AMS: 58D*     (including sub-levels)
  • AMS: 58D10    Spaces of imbeddings and immersions
  • AMS: 58D15    Manifolds of mappings
  • AMS: 58D17    Manifolds of metrics (esp. Riemannian)
  • AMS: 58D20    Measures (Gaussian, cylindrical, etc.) on manifolds of maps
  • AMS: 58D25    Equations in function spaces; evolution equations
  • AMS: 58D27    Moduli problems for differential geometric structures
  • AMS: 58D29    Moduli problems for topological structures
  • AMS: 58D30    Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
  • AMS: 58D99    None of the above, but in this section
• AMS: 58Exx    Variational problems in infinite-dimensional spaces
  AMS: 58E*     (including sub-levels)
  • AMS: 58E05    Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)
  • AMS: 58E07    Abstract bifurcation theory
  • AMS: 58E10    Applications to the theory of geodesics (problems in one independent variable)
  • AMS: 58E11    Critical metrics
  • AMS: 58E12    Applications to minimal surfaces (problems in two independent variables)
  • AMS: 58E15    Application to extremal problems in several variables; Yang-Mills functionals , etc.
  • AMS: 58E17    Pareto optimality, etc., applications to economics
  • AMS: 58E20    Harmonic maps , etc.
  • AMS: 58E30    Variational principles
  • AMS: 58E35    Variational inequalities (global problems)
• AMS: 58Hxx    Pseudogroups, differentiable groupoids and general structures on manifolds
  AMS: 58H*     (including sub-levels)
  • AMS: 58H05    Pseudogroups and differentiable groupoids
  • AMS: 58H10    Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
  • AMS: 58H15    Deformations of structures
  • AMS: 58H99    None of the above, but in this section
• AMS: 58Jxx    Partial differential equations on manifolds; differential operators
  AMS: 58J*     (including sub-levels)
  • AMS: 58J05    Elliptic equations on manifolds, general theory
  • AMS: 58J10    Differential complexes ; elliptic complexes
  • AMS: 58J15    Relations with hyperfunctions
  • AMS: 58J20    Index theory and related fixed point theorems
  • AMS: 58J22    Exotic index theories
  • AMS: 58J26    Elliptic genera
  • AMS: 58J30    Spectral flows
  • AMS: 58J32    Boundary value problems on manifolds
  • AMS: 58J35    Heat and other parabolic equation methods
  • AMS: 58J37    Perturbations; asymptotics
  • AMS: 58J40    Pseudodifferential and Fourier integral operators on manifolds
  • AMS: 58J42    Noncommutative global analysis, noncommutative residues
  • AMS: 58J45    Hyperbolic equations
  • AMS: 58J47    Propagation of singularities; initial value problems
  • AMS: 58J50    Spectral problems; spectral geometry; scattering theory
  • AMS: 58J53    Isospectrality
  • AMS: 58J60    Relations with special manifold structures (Riemannian, Finsler, etc.)
  • AMS: 58J65    Diffusion processes and stochastic analysis on manifolds
  • AMS: 58J70    Invariance and symmetry properties
  • AMS: 58J72    Correspondences and other transformation methods (e.g. Lie-Bäcklund)
  • AMS: 58J90    Applications
  • AMS: 58J99    None of the above, but in this section
• AMS: 58Kxx    Theory of singularities and catastrophe theory
  AMS: 58K*     (including sub-levels)
  • AMS: 58K05    Critical points of functions and mappings
  • AMS: 58K25    Stability
  • AMS: 58K35    Catastrophe theory
  • AMS: 58K60    Deformation of singularities
  • AMS: 58K65    Topological invariants
  • AMS: 58K70    Symmetries, equivariance
• AMS: 58Zxx    Applications to physics
  AMS: 58Z*     (including sub-levels)
  • AMS: 58Z05    Applications to physics

Letzte Änderung: 20.07.2012 Gabriele Dörflinger