2006/10/31 by Ruth Charney, John Crisp, Karen Vogtmann
Mathematics · #Algebraic number #Artin group #Automorphism #Cohomological dimension #Dimension (graph theory) #Finite group #Geometric and Algebraic Topology #Geometry and complex manifolds #Graph #Homotopy and Cohomology in Algebraic Topology #Join (topology) #Outer automorphism group #math.GR #msc:20F36
paper · pdf · doi:10.2140/gt.2007.11.2227
published as Geom. Topol. 11 (2007) 2227-2264 · Bounds on vcd improved, proof of Tits' alternative added, expository improvements, typos corrected
arxiv created 2007/05/06 · openalex publication_date 2007/11/14 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the outer automorphism group of a right-angled Artin group A in the case where the defining graph is connected and triangle-free. We give an algebraic description of Out.A / in terms of maximal join subgraphs in and prove that the Tits' alternative holds for Out.A /. We construct an analogue of outer space for Out.A / and prove that it is finite dimensional, contractible, and has a proper action of Out.A /. We show that Out.A / 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.