Loday constructions of Tambara functors
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911037278650368 |
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| author | Lindenstrauss, Ayelet Richter, Birgit Zou, Foling |
| author_facet | Lindenstrauss, Ayelet Richter, Birgit Zou, Foling |
| contents | Building on work of Hill, Hoyer and Mazur we propose an equivariant version of a Loday construction for $G$-Tambara functors where $G$ is an arbitrary finite group. For any finite simplicial $G$-set and any $G$-Tambara functor, our Loday construction is a simplicial $G$-Tambara functor. We study its properties and examples. For a circle with rotation action by a finite cyclic group our construction agrees with the twisted cyclic nerve of Blumberg, Gerhardt, Hill, and Lawson. We also show how the Loday construction for genuine commutative $G$-ring spectra relates to our algebraic one via the $\underlineπ_0$-functor. We describe Real topological Hochschild homology as such a Loday construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04216 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Loday constructions of Tambara functors Lindenstrauss, Ayelet Richter, Birgit Zou, Foling Algebraic Topology 55P91, 13D03 Building on work of Hill, Hoyer and Mazur we propose an equivariant version of a Loday construction for $G$-Tambara functors where $G$ is an arbitrary finite group. For any finite simplicial $G$-set and any $G$-Tambara functor, our Loday construction is a simplicial $G$-Tambara functor. We study its properties and examples. For a circle with rotation action by a finite cyclic group our construction agrees with the twisted cyclic nerve of Blumberg, Gerhardt, Hill, and Lawson. We also show how the Loday construction for genuine commutative $G$-ring spectra relates to our algebraic one via the $\underlineπ_0$-functor. We describe Real topological Hochschild homology as such a Loday construction. |
| title | Loday constructions of Tambara functors |
| topic | Algebraic Topology 55P91, 13D03 |
| url | https://arxiv.org/abs/2401.04216 |