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Iterated Topological Hochschild Homology of π½p at odd primes
Abstract
We compute homotopy groups of n-fold iterated topological Hochschild homology of π½p for nβ₯1 and odd primes. Identifying this as the Loday construction Tnβπ½p, we construct a bar spectral sequence computing Ο*(Tnβπ½p) and prove that this spectral sequence collapses at the E2-page. Finally, we resolve the multiplicative extensions and determine the ring structure.
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BibTeX
@misc{zha2026iterated,
title = {{Iterated Topological Hochschild Homology of $\mathbbF_p$ at odd primes}},
author = {Jiaxi Zha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05137},
eprint = {2610.05137},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05137},
}
RIS
TY - UNPB
TI - Iterated Topological Hochschild Homology of π½_p at odd primes
AU - Jiaxi Zha
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05137
UR - https://arxiv.org/abs/2610.05137
AB - We compute homotopy groups of n-fold iterated topological Hochschild homology of π½_p for nβ₯1 and odd primes. Identifying this as the Loday construction T^nβπ½_p, we construct a bar spectral sequence computing Ο_*(T^nβπ½_p) and prove that this spectral sequence collapses at the E^2-page. Finally, we resolve the multiplicative extensions and determine the ring structure.
ER -