J. Aust. Math. Soc.  74 (2003), 165-171
Betti numbers of fixed point sets and multiplicities of indecomposable summands

Semra Öztürk Kaptanoglu
  Mathematics Department
  Middle East Technical University
  Ankara 06531
  Turkey
  semra@arf.math.metu.edu.tr


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 $X^{C_n}$ 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 $n=4$.
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