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Betti numbers of fixed point sets and multiplicities of indecomposable summands
Published online by Cambridge University Press: 09 April 2009
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 XCn and the multiplicities of indecomposable summands of M considered as a kCn-module are related via a localization theorem in equivariant cohomology, where Cn is a cyclic subgroup of G of order n. Explicit formulas are given for n = 2 and n = 4.
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- Copyright © Australian Mathematical Society 2003