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arXiv · 2512.11338

Spoke topological Hochschild homology

Gabriel Angelini-Knoll·Foling Zou
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Abstract

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 B\"okstedt 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 $p$.

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Gabriel Angelini-Knoll, Foling Zou. 2025-12-12. Spoke topological Hochschild homology. https://arxiv.org/abs/2512.11338

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