Finite groups of untwisted outer automorphisms of RAAGs

Bregman, Corey; Charney, Ruth; Vogtmann, Karen

doi:10.2140/agt.2025.25.2413

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Finite groups of untwisted outer automorphisms of RAAGs

Corey Bregman, Ruth Charney and Karen Vogtmann

Algebraic & Geometric Topology 25 (2025) 2413–2440

DOI: 10.2140/agt.2025.25.2413

Abstract

For any right-angled Artin group $A_{Γ}$ , Charney, Stambaugh and Vogtmann showed that the subgroup $U^{0} (A_{Γ}) \leq Out (A_{Γ})$ generated by Whitehead automorphisms and inversions acts properly and cocompactly on a contractible space $K_{Γ}$ . We show that any finite subgroup of $U^{0} (A_{Γ})$ fixes a point of $K_{Γ}$ . This generalizes the fact that any finite subgroup of $Out (F_{n})$ fixes a point of outer space, and implies that there are only finitely many conjugacy classes of finite subgroups in $U^{0} (A_{Γ})$ .

Keywords

outer automorphisms, right-angled Artin groups

Mathematical Subject Classification

Primary: 20F28, 20F36, 20F65

References

Publication

Received: 15 October 2023

Revised: 14 February 2024

Accepted: 10 March 2024

Published: 11 August 2025

Authors

Corey Bregman
Department of Mathematics Tufts University Medford, MA United States

Ruth Charney
Department of Mathematics Brandeis University Waltham, MA United States

Karen Vogtmann
Mathematics Institute University of Warwick Coventry United Kingdom

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Volume 25, issue 4 (2025)