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arXiv · 1707.03863

Simplicial Structures Over the 3-Sphere and Generalized Higher Order Hochschild Homology

Samuel Carolus·Jacob Laubacher
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Abstract

In this paper we investigate the simplicial structure of a chain complex associated to the higher order Hochschild homology over the $3$-sphere. We also introduce the tertiary Hochschild homology corresponding to a quintuple $(A,B,C,\varepsilon,θ)$, which becomes natural after we organize the elements in a convenient manner. We establish these results by way of a bar-like resolution in the context of simplicial modules. Finally, we generalize the higher order Hochschild homology over a trio of simplicial sets, which also grants natural geometric realizations.

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Samuel Carolus, Jacob Laubacher. 2019-08-01. Simplicial Structures Over the 3-Sphere and Generalized Higher Order Hochschild Homology. https://arxiv.org/abs/1707.03863

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