Betti numbers of fixed point sets and multiplicities of indecomposable summands


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ÖZTÜRK S.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol.74, pp.165-171, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 74
  • Publication Date: 2003
  • Doi Number: 10.1017/s1446788700003220
  • Title of Journal : JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.165-171

Abstract

Let G be a finite group of even order, k be a field of characteristic 2, and M be a finitely generated kG-module. If M is realized by a compact G-Moore space X, then the Betti numbers of the fixed point set X-Cn and the multiplicities of indecomposable summands of M considered as a kC(n)-module are related via a localization theorem in equivariant cohomology, where C-n is a cyclic subgroup of G of order n. Explicit formulas are given for n = 2 and n = 4.