Bulletin of the
Korean Mathematical Society BKMS

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 stabilizers.

Keywords: Wallpaper group, Bredon homology, character, representation, $G$-CW-complex

MSC numbers: Primary 20F65, 20C15, 55N91

Supported by: The author was supported by grant PID2020-117971GB-C21 of the Spanish Ministery of Science and Innovation, and grant FQM-213 of the Junta de Andalucia.