We study the outer automorphism group of a right-angled Artin group in the case where the defining graph is connected and triangle-free. We give an algebraic description of in terms of maximal join subgraphs in and prove that the Tits’ alternative holds for . We construct an analogue of outer space for and prove that it is finite dimensional, contractible, and has a proper action of . We show that 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.
"Automorphisms of $2$–dimensional right-angled Artin groups." Geom. Topol. 11 (4) 2227 - 2264, 2007. https://doi.org/10.2140/gt.2007.11.2227