Title: Simplicial Structures for Higher Order Hochschild Homology over the $d$-Sphere,
Abstract: For $d\geq1$, we study the simplicial structure of the chain complex
associated to the higher order Hochschild homology over the $d$-sphere. We
discuss $H_\bullet^{S^d}(A,M)$ by way of a bar-like resolution
$\mathcal{B}^d(A)$ in the context of simplicial modules. Besides the general
case, we give explicit detail corresponding to $S^3$. We also present a
description of what can replace these bar-like resolutions in order to aid with
computation. The cohomology version can be done following a similar
construction, of which we make mention.