#### Volume 19, issue 7 (2019)

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Splittings and calculational techniques for higher $\mathsf{THH}$

### Irina Bobkova, Eva Höning, Ayelet Lindenstrauss, Kate Poirier, Birgit Richter and Inna Zakharevich

Algebraic & Geometric Topology 19 (2019) 3711–3753
##### Abstract

Tensoring finite pointed simplicial sets $X$ with commutative ring spectra $R$ yields important homology theories such as (higher) topological Hochschild homology and torus homology. We prove several structural properties of these constructions relating $X\otimes \left(-\right)$ to $\Sigma X\otimes \left(-\right)$ and we establish splitting results. This allows us, among other important examples, to determine ${\mathsf{THH}}_{\ast }^{\left[n\right]}\left(ℤ∕\phantom{\rule{0.3em}{0ex}}{p}^{m};ℤ∕\phantom{\rule{0.3em}{0ex}}p\right)$ for all $n\ge 1$ and for all $m\ge 2$.

##### Keywords
higher topological Hochschild homology, higher Shukla homology
Primary: 18G60
Secondary: 55P43