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.
|Number of pages||26|
|Journal||Bulletin of the Belgian Mathematical Society - Simon Stevin|
|State||Published - 2014|
Bibliographical noteFunding 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.
© 2014 Belgian Mathematical Society. All rights reserved.
- Bredon theory
- Equivariant homotopy type
- Group actions
- Homotopy actions
ASJC Scopus subject areas
- Mathematics (all)