57XX 


Manifolds and cell complexes {For complex manifolds, see 32Qxx} 

57Rxx 

Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinitedimensional manifolds, see 58Bxx} 


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; GelʹfandFuks 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 