Constructing equivariant homotopy equivalences via extension of scalars

Given a finite group $G$, we present a new algorithm to construct a $\mathbb{Z}G$-linear strong homotopy equivalence of $\mathbb{Z}G$-complexes from a $\mathbb{Z}$-linear one.

Keywords

strong homotopy equivalence, bar construction, perturbation lemma, effective homological algebra, chain complex, differential graded algebra

2010 Mathematics Subject Classification

18G10, 68W30

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The research was supported by the project MUNI/A/1103/2016.

Received 26 November 2017

Received revised 1 February 2018

Published 13 June 2018