Mathematical Sciences Classification System

57Rxx - Differential topology
{For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx}

  • 1
    57R05
    Triangulating
  • 57R10
    Smoothing
  • 57R12
    Smooth approximations
  • 57R15
    Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
  • 22
    57R17
    Symplectic and contact topology
  • 2
    57R18
    Topology and geometry of orbifolds
  • 2
    57R19
    Algebraic topology on manifolds
  • 5
    57R20
    Characteristic classes and numbers
  • 1
    57R22
    Topology of vector bundles and fiber bundles [See also 55Rxx]
  • 2
    57R25
    Vector fields, frame fields
  • 2
    57R27
    Controllability of vector fields on C and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]
  • 18
    57R30
    Foliations; geometric theory
  • 1
    57R32
    Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]
  • 2
    57R35
    Differentiable mappings
  • 57R40
    Embeddings
  • 2
    57R42
    Immersions
  • 2
    57R45
    Singularities of differentiable mappings
  • 1
    57R50
    Diffeomorphisms
  • 57R52
    Isotopy
  • 2
    57R55
    Differentiable structures
  • 16
    57R56
    Topological quantum field theories
  • 11
    57R57
    Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
  • 10
    57R58
    Floer homology
  • 57R60
    Homotopy spheres, Poincaré conjecture
  • 4
    57R65
    Surgery and handlebodies
  • 1
    57R67
    Surgery obstructions, Wall groups [See also 19J25]
  • 4
    57R70
    Critical points and critical submanifolds
  • 57R75
    O- and SO-cobordism
  • 1
    57R77
    Complex cobordism (U- and SU-cobordism) [See also 55N22]
  • 57R80
    h- and s-cobordism
  • 2
    57R85
    Equivariant cobordism
  • 57R90
    Other types of cobordism [See also 55N22]
  • 2
    57R91
    Equivariant algebraic topology of manifolds
  • 57R95
    Realizing cycles by submanifolds
  • 57R99
    None of the above, but in this section

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