Outer space for untwisted automorphisms of right-angled Artin groups

Abstract

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

Example section added, introduction modified. Final version, to appear in Geometry and Topology

References in corpus (1)

• Full-featured peak reduction in right-angled Artin groups

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