Realizing homotopy group actions

David Blanc, Debasis Sen

Research output: Contribution to journalArticlepeer-review


For any finite group G, we define the notion of a Bredon homotopy action of G, modelled on the diagram of fixed point sets (XH)H≤G for a G-space X, together with a pointed homotopy action of the group NGH/H on XH/(SH>K XK).We then describe a procedure for constructing a suitable diagram X : O op G → Top from this data, by solving a sequence of elementary lifting problems. If successful, we obtain a G-space X realizing the given homotopy information, determined up to Bredon G-homotopy type. Such lifting methods may also be used to understand other homotopy questions about group actions, such as transferring a G-Action along a map f : X → Y.

Original languageEnglish
Pages (from-to)685-710
Number of pages26
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Issue number4
StatePublished - 2014

Bibliographical note

Funding Information:
∗This research was supported by the first author’s Israel Science Foundation Grant 47377 Received by the editors in October 2013. Communicated by Y. Félix. 2010 Mathematics Subject Classification : Primary: 55P91; secondary: 55S35, 55R35, 58E40. Key words and phrases : Group actions, equivariant homotopy type, Bredon theory, obstructions, homotopy actions.

Publisher Copyright:
© 2014 Belgian Mathematical Society. All rights reserved.


  • Bredon theory
  • Equivariant homotopy type
  • Group actions
  • Homotopy actions
  • Obstructions

ASJC Scopus subject areas

  • Mathematics (all)


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