Fixed point sets and the fundamental group II: Euler characteristics

Sylvain Cappell, Shmuel Weinberger, Min Yan

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)1661-1680
Number of pages20
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume154
Issue number6
DOIs
StatePublished - Dec 1 2024

Keywords

  • Euler characteristic
  • Smith theory
  • algebraic K-theory
  • fixed points
  • group actions
  • transformation groups

ASJC Scopus subject areas

  • General Mathematics

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