#### Volume 21, issue 2 (2017)

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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