On the Bieri-Neumann-Strebel-Renz ${\Sigma }^1$-invariant of even Artin groups

Abstract

We calculate the Bieri-Neumann-Strebel-Renz invariant ${\Sigma }^1(G)$ for even Artin groups $G$ with underlying graph $\Gamma$ such that if there is a closed reduced path in $\Gamma$ with all labels bigger than 2 then the length of such path is always odd. We show that ${\Sigma }^1(G{)}^c$ is a rationally defined spherical polyhedron.

Cited by in corpus (1)

• On the $\Sigma$-invariants of Artin groups satisfying the $K(\pi ,1)$-conjecture