## Topology & Geometric Group Theory Seminar

## Fall 2009

### 1:30 – 2:30, Malott 203

Thursday, November 12

Kim Ruane, Tufts
University

*Automorphism groups of graph products*

In recent joint work with R. Charney, N. Stambaugh and A. Vijayan we
prove that a finite index subgroup of the automorphism group of a
certain type of graph product of finitely generated abelian groups is
again a graph product of finitely generated abelian groups. The
necessary condition is the "no SILS" condition discovered in previous
joint work of mine with A. Piggott and M. Gutierrez. If the original
graph product has all finite vertex groups, then this condition
implies that the outer automorphism group is finite. One consequence
of the new result is that these automorphism groups
are *virtually* CAT(0).

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