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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 $X \otimes (-)$ to $\Sigma X \otimes (-)$ and we establish splitting results. This allows us, among other important examples, to determine $THH^{[n]}_*(\mathbb{Z}/p^m; \mathbb{Z}/p)$ for all $n \geq 1$ and
for all $m \geq 2$.