Outer space for untwisted automorphisms of right-angled Artin groups

Charney, Ruth¹ ; Stambaugh, Nathaniel² ; Vogtmann, Karen³

¹ Department of Mathematics, Brandeis University, Waltham, MA 02453, United States
² Department of Mentoring, Western Governors University, General Education, Salt Lake City, UT 84107, United States
³ Mathematics Institute, University of Warwick, Zeeman Building, Coventry, CV4 7AL, United Kingdom

Geometry & topology, Tome 21 (2017) no. 2, pp. 1131-1178.

Résumé

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

Détail

DOI : 10.2140/gt.2017.21.1131

Classification : 20F65, 20F28, 20F36
Keywords: automorphisms, right-angled Artin groups

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