Bredon homology of wallpaper groups

TL;DR

This paper computes the Bredon homology of wallpaper groups using complex representation rings, providing explicit bases based on irreducible characters, which advances understanding of their algebraic topology.

Contribution

It introduces explicit calculations of Bredon homology for wallpaper groups with detailed bases, a novel contribution in the algebraic topology of these groups.

Findings

Explicit bases of homology groups provided

Homology computed with respect to finite groups family

Uses complex representation rings for calculations

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.