Projective resolutions for graph products

Details Projective resolutions for graph products Projective resolutions for graph products

1993-10-16

arxiv.org/abs/math/9310207v1

Mathematics

Group Theory

AMS-Tex, 4 pages, no figures

Scientific paper

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.

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