Automorphisms of 2–dimensional right-angled Artin groups

We study the outer automorphism group of a right-angled Artin group A in the case where the defining graph is connected and triangle-free.We give an algebraic description of Out.A / in terms of maximal join subgraphs in and prove that the Tits' alternative holds for Out.A /.We construct an analogue of outer space for Out.A / and prove that it is finite dimensional, contractible, and has a proper action of Out.A /.We show that Out.A / 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.