Automorphisms of two-dimensional right-angled Artin groups

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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