57-XX |
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Manifolds and cell complexes {For complex manifolds, see 32Qxx} |
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57Rxx |
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Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx} |
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57R05 |
Triangulating |
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57R10 |
Smoothing |
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57R12 |
Smooth approximations |
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57R15 |
Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) |
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57R17 |
Symplectic and contact topology |
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57R19 |
Algebraic topology on manifolds |
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57R20 |
Characteristic classes and numbers |
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57R22 |
Topology of vector bundles and fiber bundles [See also 55Rxx] |
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57R25 |
Vector fields, frame fields |
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57R27 |
Controllability of vector fields on $C^\infty$ and real-analytic manifolds [See also 49Qxx, 37C10, 93B05] |
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57R30 |
Foliations; geometric theory |
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57R32 |
Classifying spaces for foliations; Gelʹfand-Fuks cohomology [See also 58H10] |
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57R35 |
Differentiable mappings |
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57R40 |
Embeddings |
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57R42 |
Immersions |
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57R45 |
Singularities of differentiable mappings |
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57R50 |
Diffeomorphisms |
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57R52 |
Isotopy |
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57R55 |
Differentiable structures |
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57R56 |
Topological quantum field theories |
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57R57 |
Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX] |
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57R58 |
Floer homology |
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57R60 |
Homotopy spheres, Poincaré conjecture |
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57R65 |
Surgery and handlebodies |
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57R67 |
Surgery obstructions, Wall groups [See also 19J25] |
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57R70 |
Critical points and critical submanifolds |
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57R75 |
O- and SO-cobordism |
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57R77 |
Complex cobordism (U- and SU-cobordism) [See also 55N22] |
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57R80 |
$h$- and $s$-cobordism |
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57R85 |
Equivariant cobordism |
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57R90 |
Other types of cobordism [See also 55N22] |
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57R91 |
Equivariant algebraic topology of manifolds |
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57R95 |
Realizing cycles by submanifolds |
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57R99 |
None of the above, but in this section |