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2020 Equivariant loops on classifying spaces
Kristian Jonsson Moi
Algebr. Geom. Topol. 20(5): 2511-2552 (2020). 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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Kristian Jonsson Moi. "Equivariant loops on classifying spaces." Algebr. Geom. Topol. 20 (5) 2511 - 2552, 2020. https://doi.org/10.2140/agt.2020.20.2511

Information

Received: 7 December 2018; Revised: 15 November 2019; Accepted: 8 December 2019; Published: 2020
First available in Project Euclid: 10 November 2020

MathSciNet: MR4171572
Digital Object Identifier: 10.2140/agt.2020.20.2511

Subjects:
Primary: 55P35, 55P48, 55P91

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 5 • 2020
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