## Geometry & Topology

### Outer space for untwisted automorphisms of right-angled Artin groups

#### Abstract

For a right-angled Artin group $AΓ$, the untwisted outer automorphism group $U(AΓ)$ is the subgroup of $Out(AΓ)$ 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 $ΣΓ$ on which $U(AΓ)$ acts properly and prove that $ΣΓ$ is contractible, providing a geometric model for $U(AΓ)$ and its subgroups. We also propose a geometric model for all of $Out(AΓ)$, defined by allowing more general markings and metrics on points of $ΣΓ$.

#### Article information

Source
Geom. Topol., Volume 21, Number 2 (2017), 1131-1178.

Dates
Revised: 5 February 2016
Accepted: 25 March 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510859176

Digital Object Identifier
doi:10.2140/gt.2017.21.1131

Mathematical Reviews number (MathSciNet)
MR3626599

Zentralblatt MATH identifier
06701804

#### Citation

Charney, Ruth; Stambaugh, Nathaniel; Vogtmann, Karen. Outer space for untwisted automorphisms of right-angled Artin groups. Geom. Topol. 21 (2017), no. 2, 1131--1178. doi:10.2140/gt.2017.21.1131. https://projecteuclid.org/euclid.gt/1510859176

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