Bredon Cohomology of Polyhedral Products

Qiaofeng Zhu

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arXiv · 1811.07076

Bredon Cohomology of Polyhedral Products

Qiaofeng Zhu

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Abstract

A polyhedral product is a natural subspace of a Cartesian product, which is specified by a simplicial complex K. The automorphism group Aut(K) of K induces a group action on the polyhedral product. In this paper we study this group action and give a formula for the fixed point set of the polyhedral product for any subgroup H of Aut(K). We use the fixed point data to compute examples of Bredon cohomolohgy for small non-Abelian groups such as $D_8$ and $\Sigma_4$.

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Qiaofeng Zhu. 2018-11-17. Bredon Cohomology of Polyhedral Products. https://arxiv.org/abs/1811.07076

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