English

Equivariant loops on classifying spaces

K-Theory and Homology 2020-11-11 v1 Algebraic Topology

Abstract

We compute the homology of the space of equivariant loops on the classifying space of a simplicial monoid MM with anti-involution, provided π0(M)\pi_0 (M) is central in the homology ring of MM. The proof is similar to McDuff and Segal's proof of the group completion theorem. Then we compute the homology of the C2C_2-fixed points of a Segal-type model of the algebraic KK-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.

Keywords

Cite

@article{arxiv.1303.4528,
  title  = {Equivariant loops on classifying spaces},
  author = {Kristian Jonsson Moi},
  journal= {arXiv preprint arXiv:1303.4528},
  year   = {2020}
}
R2 v1 2026-06-21T23:44:17.969Z