Geometry & Topology
- Geom. Topol.
- Volume 11, Number 4 (2007), 2227-2264.
Automorphisms of $2$–dimensional right-angled Artin groups
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.
Geom. Topol., Volume 11, Number 4 (2007), 2227-2264.
Received: 4 August 2007
Accepted: 7 September 2007
First available in Project Euclid: 20 December 2017
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Charney, Ruth; Crisp, John; Vogtmann, Karen. Automorphisms of $2$–dimensional right-angled Artin groups. Geom. Topol. 11 (2007), no. 4, 2227--2264. doi:10.2140/gt.2007.11.2227. https://projecteuclid.org/euclid.gt/1513799981