Bredon homology of Artin groups of dihedral type

TL;DR

This paper computes the Bredon homology groups for Artin groups of dihedral type, focusing on the classifying space for virtually cyclic subgroups with coefficients in K-theory of group rings, advancing understanding in algebraic topology.

Contribution

It provides explicit calculations of Bredon homology for a specific class of Artin groups, a novel contribution to the field.

Findings

Explicit Bredon homology groups computed for dihedral Artin groups

Enhanced understanding of classifying spaces for virtually cyclic subgroups

Results applicable to algebraic K-theory and topological group actions

Abstract

For Artin groups of dihedral type, we compute the Bredon homology groups of the classifying space for the family of virtually cyclic subgroups with coefficients in the K-theory of a group ring.