Equivariant loops on classifying spaces

Moi, Kristian Jonsson

doi:10.2140/agt.2020.20.2511

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Equivariant loops on classifying spaces

Kristian Jonsson Moi

Algebraic & Geometric Topology 20 (2020) 2511–2552

DOI: 10.2140/agt.2020.20.2511

Abstract

We compute the homology of the space of equivariant loops on the classifying space of a simplicial monoid $M$ with anti-involution, provided $π_{0} (M)$ is central in the homology ring of $M$ . The proof is similar to McDuff and Segal’s proof of the group completion theorem. Then we give an analogous computation of the homology of the $C_{2}$ –fixed points of a $Γ$ –space-type delooping of an additive category with duality with respect to the sign circle. As an application we show that this fixed-point space is sometimes group complete, but in general not.

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Keywords

algebraic topology, loop space, classifying space, group completion

Mathematical Subject Classification 2010

Primary: 55P35, 55P48, 55P91

References

Publication

Received: 7 December 2018

Revised: 15 November 2019

Accepted: 8 December 2019

Published: 4 November 2020

Authors

Kristian Jonsson Moi
Department of Mathematics KTH Stockholm Sweden

Volume 20, issue 5 (2020)