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Betti numbers of fixed point sets and multiplicities of indecomposable summands

Part of: Representation theory of groups Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  09 April 2009

Semra Öztürk Kaptanoglu
Semra Öztürk Kaptanoglu
Affiliation:
Mathematics Department Middle East Technical UniversityAnkara 06531Turkey e-mail: semra@arf.math.metu.edu.tr
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Abstract

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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.

Keywords

Betti numberfixed point setMoore spacerealizable modulemultiplicityindecomposable summandlocalizationequivariant cohomology.

MSC classification

Secondary: 55M35: Finite groups of transformations (including Smith theory) 20C05: Group rings of finite groups and their modules
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 165 - 172
Copyright
Copyright © Australian Mathematical Society 2003

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