Finite graph product closure for a conjecture on the BNS-invariant of Artin groups

On the Bieri–Neumann–Strebel–Renz invariants of residually free groups

“…The Σ-invariants have been calculated for some classes of groups and sometimes in low dimensions only : Thompson group F [6], generalised Thompson groups [18], [32], braided Thompson groups [33], Houghton groups [32], some free-by-cyclic groups [16], [17], fundamental groups of compact Kähler manifolds [15], metabelian groups of finite Prüfer rank [25], some Artin groups including right angled Artin groups [2], [3], [22], [23], [24], limit groups [19], pure symmetric automorphism groups of finitely generated free groups [27], [34], some wreath products [26], some residually free groups [20], the Lodha-Moore groups [21]. In this paper we add to the list above a subclass of the class of even Artin groups.…”

“…is a free group of rank 2 [1], for Artin groups of finite type (i.e. the associated Coheter group is finite) [3]. We concentrate now on a special type of Artin groups : the even Artin groups i.e.…”

On the Bieri-Neumann-Strebel-Renz invariants of the weak commutativity construction $\X(G)$

“…Still there are some results on Σ 1 (G) for specific Artin groups by Almeida [1], Almeida and Kochloukova [2]. In [3] Almeida and Lima calculated Σ 1 (G) for Artin group of finite type ( i.e spherical type). The case of combinatorial wreath product was considered by Mendonça [34].…”