Simplicial structures over the 3-sphere and generalized higher order Hochschild homology

Document Type : Research Paper


1 Department of Mathematics, Ohio Northern University, Ohio, United States of America

2 Department of Mathematics, St. Norbert College, Wisconsin, United States of America


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 $(A,B,C,\varepsilon,\theta)$, 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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