Les groupes de triangles $(2,p,q)$ sont d\'etermine\'es par leur spectre des longueurs

TL;DR

This paper investigates the length spectra of triangle groups (2,p,q), demonstrating that these spectra uniquely determine the isometry class of the groups, thus linking geometric properties to algebraic classification.

Contribution

The paper provides a complete description of the length spectra of (2,p,q) triangle groups and proves that these spectra uniquely identify the groups up to isometry.

Findings

Length spectra are explicitly described for (2,p,q) groups.

Length spectra uniquely determine the isometry class of these groups.

The characterization links geometric spectra to algebraic group classification.

Abstract

We describe the length spectra of triangle groups $(2,p,q)$ before showing that the length spectra characterizes the isometry class of such a group.