Projections and relative hyperbolicity

TL;DR

This paper introduces a new way to define relative hyperbolicity using projection properties and provides a distance formula for these groups, akin to formulas used for mapping class groups.

Contribution

It offers an alternative definition of relative hyperbolicity based on projection properties and derives a new distance formula for relatively hyperbolic groups.

Findings

New definition of relative hyperbolicity using projections

Distance formula for relatively hyperbolic groups

Analogy with mapping class groups

Abstract

We give an alternative definition of relative hyperbolicity based on properties of closest-point projections on peripheral subgroups. We also derive a distance formula for relatively hyperbolic groups, similar to the one for mapping class groups.