Homology of subgroups of right-angled Artin groups

TL;DR

This paper investigates the (co)homology of specific normal subgroups within right-angled Artin groups, linking algebraic topology with commutative algebra of monomial ideals.

Contribution

It provides a novel description of the (co)homology of these subgroups using the algebraic framework of squarefree monomial ideals.

Findings

Explicit (co)homology descriptions for certain subgroups

Connection established between group (co)homology and monomial ideals

Framework applicable to a family of normal subgroups

Abstract

We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew) commutative algebra of squarefree monomial ideals.