| Automorphisms of two-dimensional right-angled Artin groups |
| Ruth Charney, John Crisp and Karen Vogtmann |
| Geometry & Topology 11 (2007) 2227–2264 |
We study the outer automorphism group of a right-angled Artin group AG in the case where the defining graph G is connected and triangle-free. We give an algebraic description of Out(AG) in terms of maximal join subgraphs in G and prove that the Tits' alternative holds for Out(AG). We construct an analogue of outer space for Out(AG) and prove that it is finite dimensional, contractible, and has a proper action of Out(AG). We show that Out(AG) 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. |