Abstract
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 language | English |
|---|---|
| Pages (from-to) | 685-710 |
| Number of pages | 26 |
| Journal | Bulletin of the Belgian Mathematical Society - Simon Stevin |
| Volume | 21 |
| Issue number | 4 |
| DOIs | |
| State | Published - 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.
Keywords
- Bredon theory
- Equivariant homotopy type
- Group actions
- Homotopy actions
- Obstructions
ASJC Scopus subject areas
- Mathematics (all)