Automorphisms of 2–dimensional right-angled Artin groups
By Ruth Charney, J. Crisp, Karen Vogtmann. 2006
72 citations recorded by the source corpus.
We study the outer automorphism group of a right-angled Artin group AA in the case where the defining graph A is connected and triangle-free. We give an algebraic description of Out.AA/ in terms of maximal join subgraphs in A and prove that the Tits’ alternative holds for Out.AA/. We construct an analogue of outer space for Out.AA/ and prove that it is finite dimensional, contractible, and has a proper action of Out.AA/. We show that Out.AA/ 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. 20F36; 20F65, 20F28
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/204b5076b497e195c1a947b8a47dc479d2adc74b
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Citations in the corpus
- Peak reduction and finite presentations for automorphism groups of right-angled Artin groups (2008, background): “that behave nicely with respect to combinatorial Morse functions. In particular, this should help us to better understand outer space of right-angled Artin groups, as defined in Charney–Crisp–Vogtmann [2] for triangle-free Γ. For general Γ, certain spaces of isometric actions of AΓ on CAT(0) cubical ”