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57Rxx - Differential topology

57R05 - Triangulating
57R10 - Smoothing
57R12 - Smooth approximations
57R15 - Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
57R17 - Symplectic and contact topology
57R19 - Algebraic topology on manifolds
57R20 - Characteristic classes and numbers
57R22 - Topology of vector bundles and fiber bundles
57R25 - Vector fields, frame fields
57R27 - Controllability of vector fields on $C^\infty$ and real-analytic manifolds
57R30 - Foliations; geometric theory
57R32 - Classifying spaces for foliations; Gelfand-Fuks cohomology
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
57R58 - Floer homology
57R60 - Homotopy spheres, Poincaré conjecture
57R65 - Surgery and handlebodies
57R67 - Surgery obstructions, Wall groups
57R70 - Critical points and critical submanifolds
57R75 - O- and SO-cobordism
57R77 - Complex cobordism (U- and SU-cobordism)
57R80 - $h$- and $s$-cobordism
57R85 - Equivariant cobordism
57R90 - Other types of cobordism
57R91 - Equivariant algebraic topology of manifolds
57R95 - Realizing cycles by submanifolds
57R99 - Miscellaneous
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