The Geometry of Cycles in the Cayley Diagram of a Group

TL;DR

This paper explores the geometric properties of cycles in Cayley diagrams of finitely generated groups, providing a new way to characterize hyperbolic groups through their cycle triangulations.

Contribution

It introduces a novel geometric characterization of hyperbolic groups based on triangulations of cycles in Cayley diagrams.

Findings

Triangulations of cycles reveal hyperbolic properties.

New geometric criteria for hyperbolicity.

Enhanced understanding of Cayley diagram structures.

Abstract

A study of triangulations of cycles in the Cayley diagrams of finitely generated groups leads to a new geometric characterization of hyperbolic groups.