THE BIERI-NEUMANN-STREBEL INVARIANT FOR GRAPH PRODUCTS OF GROUPS

Given a simplicial graph Delta with vertex set V and a function F that assigns to each vertex upsilon is an element of V a group G(u)psilon, the graph product G(Delta, F) is the quotient of the free product cop roduct (upsilon is an element of V) G(n)u module the normal subgroup g enerated by all commutators [G(upsilon), G(w)] with adjacent vertices upsilon w is an element of V. Using K.S. Brown's approach to the Bieri -Neumann-Strebel invariant Sigma(1)(-) via R-tree actions we give an e xplicit formula for Sigma(1)(G(Delta, F)).