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 Σ 1 pGq " H " Σ 1 pG, Qq. For a group H that is a finitely presented residually Droms RAAG we calculate Σ 1 pHq and Σ 2 pHq dis . In addition, we obtain a necessary condition for rχs to belong to Σ n pHq.