The Bieri-Neumann-Strebel invariants for graph groups
John Meier and Leonard Vanwyk

Abstract:
Given a finite simplicial graph $\cal G$, the graph group $G\cal G$ is the 
group with generators in one-to-one correspondence with the vertices of 
$\cal G$ and with relations stating two generators commute if their 
associated vertices are adjacent in $\cal G$. The Bieri-Neumann-Strebel 
invariant can be explicitly described in terms of the original graph $\cal G$ 
and hence there is an explicit description of the distribution of finitely 
generated normal subgroups of $G\cal G$ with abelian quotient. We construct 
Eilenberg-MacLane spaces for graph groups and find partial extensions of this 
work to the higher dimensional invariants.