Bredon Cohomology of Polyhedral Products

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 ${\Sigma }_4$.

34 pages, 24 figures

References in corpus (2)

• Equivariant Eilenberg-Mac Lane spectra in cyclic $p$-groups
• A spectral sequence for polyhedral products