Geometric invariants for Artin groups

Abstract

The Bieri-Neumann-Strebel invariant of a finitely generated group $G$ determines, among other things, whether or not a given normal subgroup $N$, with $G/N$ abelian, is finitely generated. We examine the BNS-invariants of “Pride groups”, a large class of groups containing the Artin groups; in particular we establish a criterion which implies that a character $\chi$ of a Pride group $G{\cal G}$ is in the BNS-invariant $\Sigma^1(G{\cal G})$.

This restricts in the case of an Artin group $A{\cal G}$ to a simple condition which implies a character is in $\Sigma^1(A{\cal G})$. As an application this can be used to compute the unit ball in the Thurston semi-norm for the complement of iterated connected sums of $(2,n)$-torus links.

1991 Mathematics Subject Classification: 20F36, 20E07.