Infinite graph product of groups II: Analytic properties

2024/12/24 by Oyakawa, Koichi
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2412.18313

Abstract

We study analytic properties of graph product of finite groups with a hyperbolic defining graph. This is done by studying dynamics on the Bowditch compactification of the extension graph, or the crossing graph, of graph product. In particular, we provide a new class of convergence groups and identify the if and only if condition for this convergence action to be geometrically finite. We also provide a new class of properly proximal groups, relatively bi-exact groups, and groups with strongly solid group von Neumann algebras.

Related

• Infinite graph product of groups I: Geometry of the extension graph
• Automorphisms of graph products of groups and acylindrical hyperbolicity
• Graphs of hyperbolic groups and a limit set intersection theorem
• Surface subgroups of graph products of groups
• Groups acting purely loxodromically on products of hyperbolic graphs