Spoke topological Hochschild homology
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910252885082112 |
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| author | Angelini-Knoll, Gabriel Zou, Foling |
| author_facet | Angelini-Knoll, Gabriel Zou, Foling |
| contents | Fix primes $p$ and $\ell$, and let $C_p$ be the cyclic group of order $p$. We compute the $C_p$-equivariant spoke topological Hochschild homology of $\underline{\mathbb{F}}_{\ell}$ and prove it exhibits a form of Bökstedt periodicity. Here spoke topological Hochschild homology is a variant of topological Hochschild homology where one replaces the circle in the construction with the unreduced suspension of $C_p$. As an application, we use this result to give a new proof of the Segal conjecture for the cyclic group of order an odd prime $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spoke topological Hochschild homology Angelini-Knoll, Gabriel Zou, Foling Algebraic Topology 55P91, 13D03, 16E40 Fix primes $p$ and $\ell$, and let $C_p$ be the cyclic group of order $p$. We compute the $C_p$-equivariant spoke topological Hochschild homology of $\underline{\mathbb{F}}_{\ell}$ and prove it exhibits a form of Bökstedt periodicity. Here spoke topological Hochschild homology is a variant of topological Hochschild homology where one replaces the circle in the construction with the unreduced suspension of $C_p$. As an application, we use this result to give a new proof of the Segal conjecture for the cyclic group of order an odd prime $p$. |
| title | Spoke topological Hochschild homology |
| topic | Algebraic Topology 55P91, 13D03, 16E40 |
| url | https://arxiv.org/abs/2512.11338 |