Strong accessibility for hyperbolic groups

TL;DR

This paper discusses a theorem showing that certain hierarchical decompositions of hyperbolic groups are finite, emphasizing the structure of hyperbolic groups with specific torsion properties.

Contribution

It provides an account of Louder and Touikan's theorem, establishing finiteness of JSJ-hierarchies in 2-torsion-free hyperbolic groups.

Findings

JSJ-hierarchies of 2-torsion-free hyperbolic groups are finite

Many hierarchies with slender JSJ-decompositions are finite

Theorem of Louder and Touikan is central to these results

Abstract

This paper aims to give an account of theorem of Louder and Touikan which shows that many hierarchies consisting of slender JSJ-decompositions are finite. In particular JSJ-hierarchies of $2$-torsion-free hyperbolic groups are always finite.