On the algebras over equivariant little disks

Michael A. Hill

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arXiv · 1709.02005

On the algebras over equivariant little disks

Michael A. Hill

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Abstract

We describe the structure present in algebras over the little disks operads for various representations of a finite group $G$, including those that are not necessarily universe or that do not contain trivial summands. We then spell out in more detail what happens for $G=C_{2}$, describing the structure on algebras over the little disks operad for the sign representation. Here we can also describe the resulting structure in Bredon homology. Finally, we produce a stable splitting of coinduced spaces analogous to the stable splitting of the product, and we use this to determine the homology of the signed James construction.

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Michael A. Hill. 2017-09-06. On the algebras over equivariant little disks. https://arxiv.org/abs/1709.02005

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