Abstract
For a finite group G of not prime power order, Oliver showed that the obstruction for a finite CW-complex F to be the fixed point set of a contractible finite G-CW-complex is determined by the Euler characteristic χ(F). (He also has similar results for compact Lie group actions.) We show that the analogous problem for F to be the fixed point set of a finite G-CW-complex of some given homotopy type is still determined by the Euler characteristic. Using trace maps on K0 [2, 7, 18], we also see that there are interesting roles for the fundamental group and the component structure of the fixed point set.
Original language | English (US) |
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Pages (from-to) | 1661-1680 |
Number of pages | 20 |
Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
Volume | 154 |
Issue number | 6 |
DOIs | |
State | Published - Dec 1 2024 |
Keywords
- Euler characteristic
- Smith theory
- algebraic K-theory
- fixed points
- group actions
- transformation groups
ASJC Scopus subject areas
- General Mathematics