#### Vol. 312, No. 1, 2021

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

### Dessislava H. Kochloukova

Vol. 312 (2021), No. 1, 149–169
##### 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
Primary: 20J05