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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.)
• 23
  57R17
  Symplectic and contact topology
• 3
  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
• 3
  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