The Bieri-Neumann-Strebel invariant for graph products of groups Original Research Article

Given a simplicial graph Δ with vertex set V and a function image that assigns to each vertex ν ε V a group Gν, the graph product G(Δ,image)is the quotient of the free product coproduct operatorgνεV Gν modulo the normal subgroup generated by all commutators [Gν, Gw] with adjacent vertices ν, w ε V. Using K.S. Brownʹs approach to the Bieri-Neumann-Strebel invariant ∑1(−) via image-tree actions we give an explicit formula for ∑1(G(Δ, image)).