La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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55-XX Algebraic topology

• 55-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 55-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 55-02 Research exposition (monographs, survey articles)
• 55-03 Historical (must also be assigned at least one classification number from Section 01)
• 55-04 Explicit machine computation and programs (not the theory of computation or programming)
• 55-06 Proceedings, conferences, collections, etc.
• 55-99 Algebraic topology (not classified at a more specific level)
• 55Mxx Classical topics [For the topology of Euclidean spaces and manifolds, see 57Nxx]
• 55Nxx Homology and cohomology theories [See also 57Txx]
• 55Pxx Homotopy theory [For simple homotopy type, see 57Q10]
  • 55P05 Homotopy extension properties, cofibrations
  • 55P10 Homotopy equivalences
  • 55P15 Classification of homotopy type
  • 55P20 Eilenberg-Mac Lane spaces
  • 55P25 Spanier-Whitehead duality
  • 55P30 Eckmann-Hilton duality
  • 55P35 Loop spaces
  • 55P40 Suspensions
  • 55P42 Stable homotopy theory, spectra
  • 55P43 Spectra with additional structure (E, A, ring spectra, etc.) [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 55P42, 55U35, 55P47
  • 55P45 H-spaces and duals
  • 55P47 Infinite loop spaces
  • 55P48 Loop space machines, operads [See also 18D50] [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 55P47, 55U35, 55P42
  • 55P55 Shape theory [See also 54C56, 55Q07]
  • 55P57 Proper homotopy theory [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 55P15, 55P99, 55P55
  • 55P60 Localization and completion
  • 55P62 Rational homotopy theory
  • 55P65 Homotopy functors
  • 55P91 Equivariant homotopy theory [See also 19L47]
  • 55P92 Relations between equivariant and nonequivariant homotopy theory [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 55P91
  • 55P99 None of the above, but in this section
• 55Qxx Homotopy groups
• 55Rxx Fiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]
• 55Sxx Operations and obstructions
• 55Txx Spectral sequences [See also 18G40, 55R20]
• 55Uxx Applied homological algebra and category theory [See also 18Gxx]

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