An equivariant generalisation of McDuff-Segal's group-completion theorem
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914816002621440 |
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| author | Hilman, Kaif |
| author_facet | Hilman, Kaif |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An equivariant generalisation of McDuff-Segal's group-completion theorem Hilman, Kaif Algebraic Topology K-Theory and Homology 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. |
| title | An equivariant generalisation of McDuff-Segal's group-completion theorem |
| topic | Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2301.10396 |