Bredon Cohomology of Polyhedral Products

Qiaofeng Zhu

Bredon Cohomology of Polyhedral Products

Algebraic Topology 2018-11-20 v1

Authors: Qiaofeng Zhu

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 $\Sigma_4$ .

Keywords

polyhedral products bredon cohomology simplicial complexes group actions fixed point sets non-abelian groups

Cite

@article{arxiv.1811.07076,
  title  = {Bredon Cohomology of Polyhedral Products},
  author = {Qiaofeng Zhu},
  journal= {arXiv preprint arXiv:1811.07076},
  year   = {2018}
}

Comments

34 pages, 24 figures

Related papers

View all related →