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The equivariant homotopy type of G-ANR’s for compact group actions

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Abstract

We prove that if G is a compact Hausdorff group then every G-ANR has the G-homotopy type of a G-CW complex. This is applied to extend the James–Segal G-homotopy equivalence theorem to the case of arbitrary compact group actions.

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Authors and Affiliations

  1. Departamento de Matematicas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510, México Distrito Federal, México

    Sergey A. Antonyan

  2. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, (Gustaf Hällströmin katu 2b), 00014, Helsinki, Finland

    Erik Elfving

Authors
  1. Sergey A. Antonyan
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  2. Erik Elfving
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Correspondence to Erik Elfving.

Additional information

The first author was supported in part by grant U42563-F from CONACYT (Mexico).

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Antonyan, S.A., Elfving, E. The equivariant homotopy type of G-ANR’s for compact group actions. manuscripta math. 124, 275–297 (2007). https://doi.org/10.1007/s00229-007-0108-0

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