Relative Untwisted Outer Space for Right-Angled Artin Groups

2025/03/12 by Adrien Abgrall, Abgrall, Adrien · 1 citation
Mathematics · Physics and Astronomy · #20F28 (Primary) 20F36 #20F65 (Secondary) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2503.09588

openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

For G, H two finite collections of finitely generated subgroups of a right-angled Artin group A, the untwisted McCool group U(A; G, Ht) is the subgroup of untwisted outer automorphisms of A preserving the conjugacy class of each element of G and acting trivially up to conjugacy on each element of H. We prove that when the elements of G are standard subgroups of A, U(A; G, Ht) acts properly cocompactly on a finite-dimensional subcomplex of the spine of untwisted outer space for A, providing a geometric model for this group and proof that it is of type VF.

Cited by

• The McCullough-Miller complex for right angled Artin groups

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