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arXiv · 1303.4528

Equivariant loops on classifying spaces

Kristian Jonsson Moi
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Abstract

We compute the homology of the space of equivariant loops on the classifying space of a simplicial monoid $M$ with anti-involution, provided $\pi_0 (M)$ 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 compute the homology of the $C_2$-fixed points of a Segal-type model of the algebraic $K$-theory of an additive category with duality. As an application we show that this fixed point space is sometimes group complete, but not in general.

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Kristian Jonsson Moi. 2013-03-19. Equivariant loops on classifying spaces. https://doi.org/10.2140/agt.2020.20.2511

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