Mathematical Sciences Classification System
55Pxx - Homotopy theory
{For simple homotopy type, see 57Q10}
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55P05Homotopy extension properties, cofibrations
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55P10Homotopy equivalences
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55P15Classification of homotopy type
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55P20Eilenberg-Mac Lane spaces
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55P25Spanier-Whitehead duality
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55P30Eckmann-Hilton duality
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55P35Loop spaces
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55P40Suspensions
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55P42Stable homotopy theory, spectra
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55P43Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
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55P45$H$-spaces and duals
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55P47Infinite loop spaces
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55P48Loop space machines, operads [See also 18D50]
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55P50String topology
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55P55
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55P57Proper homotopy theory
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55P60Localization and completion
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55P62Rational homotopy theory
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55P65Homotopy functors
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55P91Equivariant homotopy theory [See also 19L47]
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55P92Relations between equivariant and nonequivariant homotopy theory
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55P99None of the above, but in this section