On the Bieri-Neumann-Strebel-Renz invariants and limit groups over Droms RAAGs

Abstract

For a group $G$ that is a limit group over Droms RAAGs such that $G$ has trivial center, we show that ${\Sigma }^1(G)=\varnothing ={\Sigma }^1(G,\mathbb{Q})$. For a group $H$ that is a finitely presented residually Droms RAAG we calculate ${\Sigma }^1(H)$ and ${\Sigma }^2(H{)}_{dis}$. In addition, we obtain a necessary condition for $[\chi ]$ to belong to ${\Sigma }^n(H)$.