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Introduction to Geometric Group Theory |
| August 27, 2007 to August 31, 2007 |
| Organized By: Mladen Bestvina, Jon McCammond, Michah Sageev, Karen Vogtmann |
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| Parent Programs: |
| Geometric Group Theory |
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| Return to Workshop Description |
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Automorphisms of Graph Products
Tuesday August 28, 2007
02:00PM - 02:50PM
Speakers:
Kim Ruane
Abstract:
In this talk we will discuss the structure of the automorphism group of a graph product of finitely generated abelian groups. We will mostly keep the discussion focused on the special case of right-angled Coxeter groups but many of our results are true in more generality. Tits proved that the full automorphism group of a right-angled Coxeter group splits as a semi-direct product of the conjugating automorphisms and "the rest" (which is finite in this case). Using work of Laurence, the group of conjugating automorphisms of a graph product of finitely generated abelian groups is generated by partial conjugations. In joint work with A. Piggott and M. Gutierrez we show this subgroup of the automorphism group splits even further. In particular, there is a semi-direct product decomposition with the inner automorphisms as a factor. We will spend the majority of the talk discussing some interesting applications of this result. For example, we give a simple graph-theoretic criterion which characterizes when the outer automorphism group of a right-angled Coxeter group is infinite.
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