57Rxx

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


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