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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