Mathematical Sciences Classification System

55Pxx - Homotopy theory
{For simple homotopy type, see 57Q10}

  • 55P05
    Homotopy extension properties, cofibrations
  • 1
    55P10
    Homotopy equivalences
  • 1
    55P15
    Classification of homotopy type
  • 55P20
    Eilenberg-Mac Lane spaces
  • 55P25
    Spanier-Whitehead duality
  • 55P30
    Eckmann-Hilton duality
  • 1
    55P35
    Loop spaces
  • 55P40
    Suspensions
  • 4
    55P42
    Stable homotopy theory, spectra
  • 2
    55P43
    Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
  • 55P45
    $H$-spaces and duals
  • 55P47
    Infinite loop spaces
  • 9
    55P48
    Loop space machines, operads [See also 18D50]
  • 55P50
    String topology
  • 55P55
    Shape theory [See also 54C56, 55Q07]
  • 55P57
    Proper homotopy theory
  • 3
    55P60
    Localization and completion
  • 5
    55P62
    Rational homotopy theory
  • 2
    55P65
    Homotopy functors
  • 5
    55P91
    Equivariant homotopy theory [See also 19L47]
  • 55P92
    Relations between equivariant and nonequivariant homotopy theory
  • 55P99
    None of the above, but in this section

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