Betti numbers of fixed point sets and multiplicities of indecomposable summands

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


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.