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arXiv · 2301.10396

An equivariant generalisation of McDuff-Segal's group-completion theorem

Kaif Hilman
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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.

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Kaif Hilman. 2023-01-25. An equivariant generalisation of McDuff-Segal's group-completion theorem. https://arxiv.org/abs/2301.10396

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