An equivariant generalisation of McDuff-Segal's group-completion theorem
Algebraic Topology
2024-05-31 v2 K-Theory and Homology
Abstract
In this short note, we prove a G-equivariant generalisation of McDuff-Segal's group-completion theorem for finite groups G. A new complication regarding genuine equivariant localisations arises and we resolve this by isolating a simple condition on the homotopy groups of E-infinity-rings in G-spectra. We check that this condition is satisfied when our inputs are a suitable variant of E-infinity-monoids in G-spaces via the existence of multiplicative norm structures, thus giving a localisation formula for their associated G-spherical group rings.
Keywords
Cite
@article{arxiv.2301.10396,
title = {An equivariant generalisation of McDuff-Segal's group-completion theorem},
author = {Kaif Hilman},
journal= {arXiv preprint arXiv:2301.10396},
year = {2024}
}
Comments
21 pages; v2 final accepted version, minor corrections, significant expositional improvements, included a new technical appendix