Outer space for untwisted automorphisms of right-angled artin groups

Abstract

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 v 7↦ vw with vw D wv). We define a space ΣΓ on which U (AΓ) acts properly and prove that ΣΓ is con-tractible, 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.