Geometry & Topology

Outer space for untwisted automorphisms of right-angled Artin groups

Ruth Charney, Nathaniel Stambaugh, and Karen Vogtmann

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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 vvw 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
Received: 23 September 2015
Revised: 5 February 2016
Accepted: 25 March 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 20F28: Automorphism groups of groups [See also 20E36] 20F36: Braid groups; Artin groups

Keywords
automorphisms right-angled Artin groups

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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