Divergence spectra and Morse boundaries of relatively hyperbolic groups

2016/11/15 by Tran, Hung Cong
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1611.05005

Abstract

We introduce a new quasi-isometry invariant, called the divergence spectrum, to study finitely generated groups. We compare the concept of divergence spectrum with the other classical notions of divergence and we examine the divergence spectra of relatively hyperbolic groups. We show the existence of an infinite collection of right-angled Coxeter groups which all have exponential divergence but they all have different divergence spectra. We also study Morse boundaries of relatively hyperbolic groups and examine their connection with Bowditch boundaries.

Related

• Divergence of finitely presented groups
• Divergence in lattices in semisimple Lie groups and graphs of groups
• Random divergence of groups
• Divergence, thick groups, and short conjugators
• Quasiconformal Maps between Bowditch Boundaries of Relatively Hyperbolic Groups