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arXiv · 2610.05137

Iterated Topological Hochschild Homology of $\mathbb{F}_p$ at odd primes

Jiaxi Zha
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Abstract

We compute homotopy groups of $n$-fold iterated topological Hochschild homology of $\mathbb{F}_p$ for $n\geq1$ and odd primes. Identifying this as the Loday construction $T^n\otimes\mathbb{F}_p$, we construct a bar spectral sequence computing $π_*(T^n\otimes\mathbb{F}_p)$ and prove that this spectral sequence collapses at the $E^2$-page. Finally, we resolve the multiplicative extensions and determine the ring structure.

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Jiaxi Zha. 2026-10-04. Iterated Topological Hochschild Homology of $\mathbb{F}_p$ at odd primes. https://arxiv.org/abs/2610.05137

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