Dynamical Tits alternative for groups of almost automorphisms of trees

2024/12/11 by Vio, Martín Gilabert
#20F99 (Primary) 20F65 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2412.08784

Abstract

We prove a dynamical variant of the Tits alternative for the group of almost automorphisms of a locally finite tree T: a group of almost automorphisms of T either contains a nonabelian free group playing ping-pong on the boundary ∂ T, or the action of the group on ∂ T preserves a probability measure. This generalises to all groups of tree almost automorphisms a result of S. Hurtado and E. Militon for Thompson's group V, with a hopefully simpler proof.

Related

• Simple groups of automorphisms of trees determined by their actions on finite subtrees
• Conjugacy and Dynamics in Almost Automorphism Groups of Trees
• No Tits alternative for cellular automata
• Topological models of finite type for tree almost automorphism groups
• Groups acting on trees with Tits' independence property (P)