Equivariant self-homotopy equivalences of product spaces

Let G be a finite group. We study the group of G-equivariant self-homotopy equivalences of product of G-spaces. For a product of n-spaces, we represent it as product of n-subgroups under the assumption of equivariant reducibility. Further we describe each factor as a split short exact sequence. Also...

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Bibliographic Details
Published in:arXiv.org 2022-06
Main Authors: Dutta, Gopal Chandra, Sen, Debasis, Ajay Singh Thakur
Format: Article
Language:English
Subjects:
Equivalence
Group theory
Subgroups
Online Access:Get full text
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Summary:Let G be a finite group. We study the group of G-equivariant self-homotopy equivalences of product of G-spaces. For a product of n-spaces, we represent it as product of n-subgroups under the assumption of equivariant reducibility. Further we describe each factor as a split short exact sequence. Also, we obtain an another kind of factorisation, called \(LU\) type decomposition, as product of two subgroups.
ISSN:2331-8422