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
  • 57N05 Topology of E², 2-manifolds
  • 57N10 Topology of general 3-manifolds [See also 57Mxx]
  • 57N12 Topology of E³ and S³ [See also 57M40]
  • 57N13 Topology of E⁴, 4-manifolds [See also 14Jxx, 32Jxx]
  • 57N15 Topology of Eⁿ, n-manifolds (4 < n < )
  • 57N16 Geometric structures on manifolds [See also 57M50] [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 57M50, 57N05, 57N10, 57N13, 57N15, 57N70
  • 57N17 Topology of topological vector spaces
  • 57N20 Topology of infinite-dimensional manifolds [See also 58Bxx]
  • 57N25 Shapes [See also 54C56, 55P55, 55Q07]
  • 57N30 Engulfing
  • 57N35 Embeddings and immersions
  • 57N37 Isotopy and pseudo-isotopy
  • 57N40 Neighborhoods of submanifolds
  • 57N45 Flatness and tameness
  • 57N50 S^n-1 Eⁿ, Schoenflies problem
  • 57N55 Microbundles and block bundles [See also 55R60, 57Q50]
  • 57N60 Cellularity
  • 57N65 Algebraic topology of manifolds
  • 57N70 Cobordism and concordance
  • 57N75 General position and transversality
  • 57N80 Stratifications
  • 57N99 None of the above, but in this section
• 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]
• 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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