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 [See also 55Rxx]


57R25  Vector fields, frame fields


57R27  Controllability of vector fields on $C^\infty$ and realanalytic manifolds [See also 49Qxx, 37C10, 93B05]


57R30  Foliations; geometric theory


57R32  Classifying spaces for foliations; GelfandFuks 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 SeibergWitten invariants [See also 58XX]


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  O and SOcobordism


57R77  Complex cobordism (U and SUcobordism) [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

