Bredon homology of wallpaper groups

Abstract

In this paper we compute the Bredon homology of wallpaper groups with respect to the family of finite groups and with coefficients in the complex representation ring. We provide explicit bases of the homology groups in terms of irreducible characters of the representation rings of the stabilizers.

Computations in $$C_{pq}$$ C pq -Bredon cohomology

“…Remark 2.14 (Further accesible examples of low dimension). We mention for the sake of utility the following illustrative examples of computations of Bredon cohomology in low dimension: [23], [22]. The first computation of the Bredon chain and cochain complex was done in [58].…”