Projective resolutions for graph products

by Daniel E. Cohen


Abstract: Let \Gamma be a finite graph together with a group G_v at 
each vertex v. The graph product G(\Gamma) is obtained from the free 
product of all G_v by factoring out by the normal subgroup generated 
by \{g^{-1}h^{-1}gh; g \in G_v, h \in G_w\} for all adjacent v, w. 

In this note we construct a projective resolution for G(\Gamma) given 
projective resolutions for each G_v, and obtain some applications.