Finite groups of untwisted outer automorphisms of RAAGs

2023/08/18 by Bregman, Corey, Charney, Ruth, Vogtmann, Karen
#20F28 #20F36 #20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2308.09222

Abstract

For any right-angled Artin group A_Γ, Charney--Stambaugh--Vogtmann showed that the subgroup U⁰(A_Γ) \leqOut(A_Γ) generated by Whitehead automorphisms and inversions acts properly and cocompactly on a contractible space K_Γ. In the present paper we show that any finite subgroup of U⁰(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 U⁰(A_Γ).

Related

• Outer space and finiteness properties for symmetric automorphisms of RAAGs, and generalisations
• Outer space for RAAGs
• Relative Untwisted Outer Space for Right-Angled Artin Groups
• Subgroups and quotient groups of automorphism groups of RAAGs
• Infinite groups acting faithfully on the outer automorphism group of a right-angled Artin group