La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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57-XX Manifolds and cell complexes [For complex manifolds, see 32Qxx]

• 57-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 57-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 57-02 Research exposition (monographs, survey articles)
• 57-03 Historical (must also be assigned at least one classification number from Section 01)
• 57-04 Explicit machine computation and programs (not the theory of computation or programming)
• 57-06 Proceedings, conferences, collections, etc.
• 57-99 Manifolds and cell complexes (not classified at a more specific level)
• 57Mxx Low-dimensional topology
• 57Nxx Topological manifolds
• 57Pxx Generalized manifolds [See also 18F15]
• 57Qxx PL-topology
• 57Rxx Differential topology [For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional 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 [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 57R15
  • 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 and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]
  • 57R30 Foliations; geometric theory
  • 57R32 Classifying spaces for foliations; Gelfand-Fuks 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 [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 57R57, 58D29
  • 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
  • 57R58 Floer homology [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 57R57, 55N35, 58E05
  • 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 SO-cobordism
  • 57R77 Complex cobordism (U- and SU-cobordism) [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
• 57Sxx Topological transformation groups [See also 20F34, 22-XX, 37-XX, 54H15, 58D05]
• 57Txx Homology and homotopy of topological groups and related structures

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