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

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

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In this paper, we investigate the simplicial structure of a chain complex associated to the higher order Hochschild homology over the 3" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(51, 51, 51); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; position: relative;">33-sphere. We also introduce the tertiary Hochschild homology corresponding to a quintuple (A,B,C,ε,θ)" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(51, 51, 51); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; position: relative;">(A,B,C,ε,θ)(A,B,C,ε,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.

Publication Date

Summer 2021

Keywords

Higher order Hochschild homology, pre-simplicial algebras, deformations

Comments

Carolus, S., Laubacher, J. (2021). Simplicial structures over the 3-sphere and generalized higher order Hochschild homology. Categories and General Algebraic Structures with Applications, 15(1), 93-143. doi: 10.52547/cgasa.15.1.93

doi: 10.52547/CGASA.15.1.93

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

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