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2007 Automorphisms of $2$–dimensional right-angled Artin groups
Ruth Charney, John Crisp, Karen Vogtmann
Geom. Topol. 11(4): 2227-2264 (2007). DOI: 10.2140/gt.2007.11.2227

Abstract

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

Information

Received: 4 August 2007; Accepted: 7 September 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1152.20032
MathSciNet: MR2372847
Digital Object Identifier: 10.2140/gt.2007.11.2227

Subjects:
Primary: 20F36
Secondary: 20F28, 20F65

Rights: Copyright © 2007 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2007
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