Homology of even Artin kernels

TL;DR

This paper computes the homology groups of even Artin kernels and FC-type Artin groups with field coefficients, providing explicit results in characteristic zero and partial insights in prime characteristic.

Contribution

It offers explicit homology computations for even Artin kernels and FC-type Artin groups, advancing understanding of their algebraic topology.

Findings

Homology groups computed explicitly for characteristic zero.

Partial results obtained for prime characteristic.

Enhanced understanding of algebraic topology of Artin groups.

Abstract

We explicitly compute the homology groups with coefficients in a field of characteristic zero of cocyclic subgroups or even Artin groups of FC-type. We also give some partial results in the case when the coefficients are taken in a field of prime characteristic.