Geodesic
Finite groups of untwisted outer automorphisms of RAAGs
Bregman, Corey1 ; Charney, Ruth2 ; Vogtmann, Karen3
1Department of Mathematics, Tufts University, Medford, MA, United States
2Department of Mathematics, Brandeis University, Waltham, MA, United States
3Mathematics Institute, University of Warwick, Coventry, United Kingdom
Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2413-2440
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For any right-angled Artin group AΓ, Charney, Stambaugh and Vogtmann showed that the subgroup U0(AΓ) ≤ Out ⁡ (AΓ) generated by Whitehead automorphisms and inversions acts properly and cocompactly on a contractible space KΓ. We show that any finite subgroup of U0(AΓ) fixes a point of KΓ. This generalizes the fact that any finite subgroup of Out ⁡ (Fn) fixes a point of outer space, and implies that there are only finitely many conjugacy classes of finite subgroups in U0(AΓ).

DOI : 10.2140/agt.2025.25.2413
Keywords: outer automorphisms, right-angled Artin groups

Bregman, Corey  1   ; Charney, Ruth  2   ; Vogtmann, Karen  3

1 Department of Mathematics, Tufts University, Medford, MA, United States
2 Department of Mathematics, Brandeis University, Waltham, MA, United States
3 Mathematics Institute, University of Warwick, Coventry, United Kingdom 
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Bregman, Corey; Charney, Ruth; Vogtmann, Karen. Finite groups of untwisted outer automorphisms of RAAGs. Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2413-2440. doi: 10.2140/agt.2025.25.2413

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