Mathematical Sciences Classification System
57Rxx - Differential topology
{For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx}
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57R05Triangulating
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57R10Smoothing
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57R12Smooth approximations
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57R15Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
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57R17Symplectic and contact topology
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57R18Topology and geometry of orbifolds
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57R19Algebraic topology on manifolds
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57R20Characteristic classes and numbers
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57R22Topology of vector bundles and fiber bundles [See also 55Rxx]
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57R25Vector fields, frame fields
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57R27
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57R30Foliations; geometric theory
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57R32Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]
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57R35Differentiable mappings
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57R40Embeddings
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57R42Immersions
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57R45Singularities of differentiable mappings
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57R50Diffeomorphisms
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57R52Isotopy
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57R55Differentiable structures
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57R56Topological quantum field theories
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57R57Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
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57R58Floer homology
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57R60Homotopy spheres, Poincaré conjecture
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57R65Surgery and handlebodies
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57R67Surgery obstructions, Wall groups [See also 19J25]
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57R70Critical points and critical submanifolds
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57R75O- and SO-cobordism
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57R77Complex cobordism (U- and SU-cobordism) [See also 55N22]
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57R80h- and s-cobordism
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57R85Equivariant cobordism
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57R90Other types of cobordism [See also 55N22]
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57R91Equivariant algebraic topology of manifolds
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57R95Realizing cycles by submanifolds
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57R99None of the above, but in this section