Volume 20, issue 5 (2020)

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Equivariant loops on classifying spaces

Kristian Jonsson Moi

Algebraic & Geometric Topology 20 (2020) 2511–2552

We compute the homology of the space of equivariant loops on the classifying space of a simplicial monoid M with anti-involution, provided π0(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 C2–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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algebraic topology, loop space, classifying space, group completion
Mathematical Subject Classification 2010
Primary: 55P35, 55P48, 55P91
Received: 7 December 2018
Revised: 15 November 2019
Accepted: 8 December 2019
Published: 4 November 2020
Kristian Jonsson Moi
Department of Mathematics