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

Dessislava H. Kochloukova

Vol. 312 (2021), No. 1, 149–169

DOI: 10.2140/pjm.2021.312.149

Abstract

We calculate the Bieri–Neumann–Strebel–Renz invariant ${\Sigma }^1\left(G\right)$ 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 a path is always odd. We show that ${\Sigma }^1{\left(G\right)}^c$ is a rationally defined spherical polyhedron.

Keywords

even Artin groups, $\Sigma$-invariants

Mathematical Subject Classification

Primary: 20J05

Milestones

Received: 21 October 2020

Revised: 13 February 2021

Accepted: 15 February 2021

Published: 4 August 2021