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Automorphisms of two-dimensional right-angled Artin groups

Ruth Charney·John Crisp·Karen Vogtmann
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Abstract

We study the outer automorphism group of a right-angled Artin group A_G in the case where the defining graph G is connected and triangle-free. We give an algebraic description of Out(A_G) in terms of maximal join subgraphs in G and prove that the Tits' alternative holds for Out(A_G). We construct an analogue of outer space for Out(A_G) and prove that it is finite dimensional, contractible, and has a proper action of Out(A_G). We show that Out(A_G) has finite virtual cohomological dimension, give upper and lower bounds on this dimension and construct a spine for outer space realizing the most general upper bound.

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Ruth Charney, John Crisp, Karen Vogtmann. 2007-05-06. Automorphisms of two-dimensional right-angled Artin groups. https://doi.org/10.2140/gt.2007.11.2227

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