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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.
We study the Bieri-Neumann-Strebel-Renz invariants and we prove the following criterion: for groups $H$ and $K$ of type $FP_n$ such that $[H,H] subseteq K subseteq H$ and a character $chi : K to mathbb{R}$ with $chi([H,H]) = 0$ we have $[chi] in Sigm
For a group $G$ that is a limit group over Droms RAAGs such that $G$ has trivial center, we show that $Sigma^1(G) = emptyset = Sigma^1(G, mathbb{Q})$. For a group $H$ that is a finitely presented residually Droms RAAG we calculate $Sigma^1(H)$ and $S
For a finitely generated group $G$ we calculate the Bieri-Neumann-Strebel-Renz invariant $Sigma^1(X(G))$ for the weak commutativity construction $X(G)$. Identifying $S(X(G))$ with $S(X(G) / W(G))$ we show $Sigma^2(X(G),Z) subseteq Sigma^2(X(G)/ W(G),
We compute the BNS-invariant for the pure symmetric automorphism groups of right-angled Artin groups. We use this calculation to show that the pure symmetric automorphism group of a right-angled Artin group is itself not a right-angled Artin group pr
The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators of any Artin group generate an obvious right-angled Artin subgroup. We consider a larger set of elements consisting of all the centers of the irreducible s