Volume 21, issue 2 (2017)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Outer space for untwisted automorphisms of right-angled Artin groups

Ruth Charney, Nathaniel Stambaugh and Karen Vogtmann

Geometry & Topology 21 (2017) 1131–1178
Abstract

For a right-angled Artin group ${A}_{\Gamma }$, the untwisted outer automorphism group $U\left({A}_{\Gamma }\right)$ is the subgroup of $Out\left({A}_{\Gamma }\right)$ generated by all of the Laurence–Servatius generators except twists (where a twist is an automorphism of the form $v↦vw$ with $vw=wv$). We define a space ${\Sigma }_{\Gamma }$ on which $U\left({A}_{\Gamma }\right)$ acts properly and prove that ${\Sigma }_{\Gamma }$ is contractible, providing a geometric model for $U\left({A}_{\Gamma }\right)$ and its subgroups. We also propose a geometric model for all of $Out\left({A}_{\Gamma }\right)$, defined by allowing more general markings and metrics on points of ${\Sigma }_{\Gamma }$.

Keywords
automorphisms, right-angled Artin groups
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20F28, 20F36