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Please note that in the second half of 2009, MSC2010 is deployed in the production of ZMATH and will become official standard in January 2010.

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57-XX Manifolds and cell complexes {For complex manifolds, see 32Qxx} → ZMATH
57Rxx Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx} → ZMATH
57R05 Triangulating → ZMATH
57R10 Smoothing → ZMATH
57R12 Smooth approximations → ZMATH
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) → ZMATH
57R17 Symplectic and contact topology → ZMATH
57R19 Algebraic topology on manifolds → ZMATH
57R20 Characteristic classes and numbers → ZMATH
57R22 Topology of vector bundles and fiber bundles [See also 55Rxx] → ZMATH
57R25 Vector fields, frame fields → ZMATH
57R27 Controllability of vector fields on $C^\infty$ and real-analytic manifolds [See also 49Qxx, 37C10, 93B05] → ZMATH
57R30 Foliations; geometric theory → ZMATH
57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10] → ZMATH
57R35 Differentiable mappings → ZMATH
57R40 Embeddings → ZMATH
57R42 Immersions → ZMATH
57R45 Singularities of differentiable mappings → ZMATH
57R50 Diffeomorphisms → ZMATH
57R52 Isotopy → ZMATH
57R55 Differentiable structures → ZMATH
57R56 Topological quantum field theories → ZMATH
57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX] → ZMATH
57R58 Floer homology → ZMATH
57R60 Homotopy spheres, PoincarĂ© conjecture → ZMATH
57R65 Surgery and handlebodies → ZMATH
57R67 Surgery obstructions, Wall groups [See also 19J25] → ZMATH
57R70 Critical points and critical submanifolds → ZMATH
57R75 O- and SO-cobordism → ZMATH
57R77 Complex cobordism (U- and SU-cobordism) [See also 55N22] → ZMATH
57R80 $h$- and $s$-cobordism → ZMATH
57R85 Equivariant cobordism → ZMATH
57R90 Other types of cobordism [See also 55N22] → ZMATH
57R91 Equivariant algebraic topology of manifolds → ZMATH
57R95 Realizing cycles by submanifolds → ZMATH
57R99 None of the above, but in this section → ZMATH
Abel prize 2010
I. M. Gelfand 1913-2009

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