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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Outer space for untwisted automorphisms of right-angled Artin groups

Ruth Charney, Nathaniel Stambaugh and Karen Vogtmann

Geometry & Topology 21 (2017) 1131–1178

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.

automorphisms, right-angled Artin groups
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20F28, 20F36
Received: 23 September 2015
Revised: 5 February 2016
Accepted: 25 March 2016
Published: 17 March 2017
Proposed: Ian Agol
Seconded: Martin Bridson, Bruce Kleiner
Ruth Charney
Department of Mathematics
Brandeis University
Waltham, MA 02453
United States
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
United Kingdom