Automorphisms of two-dimensional right-angled Artin groups
Group Theory
2014-11-11 v2
Abstract
We study the outer automorphism group of a right-angled Artin group A_G in the case where the defining graph G is connected and triangle-free. We give an algebraic description of Out(A_G) in terms of maximal join subgraphs in G and prove that the Tits' alternative holds for Out(A_G). We construct an analogue of outer space for Out(A_G) and prove that it is finite dimensional, contractible, and has a proper action of Out(A_G). We show that Out(A_G) 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.
Cite
@article{arxiv.math/0610980,
title = {Automorphisms of two-dimensional right-angled Artin groups},
author = {Ruth Charney and John Crisp and Karen Vogtmann},
journal= {arXiv preprint arXiv:math/0610980},
year = {2014}
}
Comments
Bounds on vcd improved, proof of Tits' alternative added, expository improvements, typos corrected