Outer space for untwisted automorphisms of right-angled Artin groups

Charney, Ruth; Stambaugh, Nathaniel; Vogtmann, Karen

doi:10.2140/gt.2017.21.1131

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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

DOI: 10.2140/gt.2017.21.1131

Abstract

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

Keywords

automorphisms, right-angled Artin groups

Mathematical Subject Classification 2010

Primary: 20F65

Secondary: 20F28, 20F36

References

Publication

Received: 23 September 2015

Revised: 5 February 2016

Accepted: 25 March 2016

Published: 17 March 2017

Proposed: Ian Agol

Seconded: Martin Bridson, Bruce Kleiner

Authors

Ruth Charney
Department of Mathematics Brandeis University Waltham, MA 02453 United States
http://people.brandeis.edu/~charney/
Nathaniel Stambaugh
Department of Mentoring Western Governors University General Education Salt Lake City, UT 84107 United States

Karen Vogtmann
Mathematics Institute University of Warwick Zeeman Building Coventry CV4 7AL United Kingdom
https://www2.warwick.ac.uk/fac/sci/maths/people/staff/karen\_vogtmann/

Volume 21, issue 2 (2017)