Geometry & Topology

Outer space for untwisted automorphisms of right-angled Artin groups

Ruth Charney, Nathaniel Stambaugh, and Karen Vogtmann

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

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

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

automorphisms right-angled Artin groups


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.

Export citation


  • I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045–1087
  • K-U Bux, R Charney, K Vogtmann, Automorphisms of two-dimensional RAAGS and partially symmetric automorphisms of free groups, Groups Geom. Dyn. 3 (2009) 541–554
  • R Charney, An introduction to right-angled Artin groups, Geom. Dedicata 125 (2007) 141–158
  • R Charney, J Crisp, K Vogtmann, Automorphisms of $2$–dimensional right-angled Artin groups, Geom. Topol. 11 (2007) 2227–2264
  • R Charney, K Vogtmann, Finiteness properties of automorphism groups of right-angled Artin groups, Bull. Lond. Math. Soc. 41 (2009) 94–102
  • R Charney, K Vogtmann, Subgroups and quotients of automorphism groups of RAAGs, from “Low-dimensional and symplectic topology” (M Usher, editor), Proc. Sympos. Pure Math. 82, Amer. Math. Soc., Providence, RI (2011) 9–27
  • M Culler, K Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986) 91–119
  • M B Day, Peak reduction and finite presentations for automorphism groups of right-angled Artin groups, Geom. Topol. 13 (2009) 817–855
  • M B Day, Full-featured peak reduction in right-angled Artin groups, Algebr. Geom. Topol. 14 (2014) 1677–1743
  • F Haglund, D T Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008) 1551–1620
  • A H M Hoare, Coinitial graphs and Whitehead automorphisms, Canad. J. Math. 31 (1979) 112–123
  • M R Laurence, A generating set for the automorphism group of a graph group, J. London Math. Soc. 52 (1995) 318–334
  • D Quillen, Higher algebraic $K$–theory, I, from “Algebraic $K$–theory, I: Higher $K$–theories” (H Bass, editor), Lecture Notes in Math. 341, Springer, Berlin (1973) 85–147
  • H Servatius, Automorphisms of graph groups, J. Algebra 126 (1989) 34–60
  • A Vijayan, Compactifying the space of length functions of a right-angled Artin group, preprint (2015)