HIGHER GENERATION SUBGROUP SETS AND THE SIGMA-INVARIANTS OF GRAPH GROUPS

We present a general condition, based on the idea of n-generating subg roup sets, which implies that a given character chi is an element of H om(G, R) represents a point in the homotopical or homological C-invari ants of the group G. Let G be a finite simplicial graph, (G) over cap the flag complex induced by G, and GB the graph group, or 'right angle d Artin group', defined by G. We use our result on n-generating subgro up sets to describe the homotopical and homological Sigma-invariants o f GG in terms of the topology of subcomplexes of (G) over cap. In part icular, this work determines the finiteness properties of kernels of m aps from graph groups to abelian groups. This is the first complete co mputation of the C-invariants for a family of groups whose higher inva riants are not determined - either implicitly or explicitly - by Sigma (1).