Fibonacci groups, F(2,n), are hyperbolic for n odd and n >= 11

TL;DR

This paper proves that Fibonacci groups F(2,n) are hyperbolic for odd n greater than or equal to 11, using curvature arguments and isoperimetric inequalities to establish hyperbolicity.

Contribution

The paper demonstrates hyperbolicity of F(2,n) for odd n >= 11 through a novel application of curvature and isoperimetric techniques.

Findings

F(2,n) is hyperbolic for odd n >= 11

Curvature argument applied to van Kampen diagrams

Linear isoperimetric inequality established

Abstract

We prove that the Fibonacci group, F(2,n), for n odd and n >= 11 is hyperbolic. We do this by applying a curvature argument to an arbitrary van Kampen diagram of F(2,n) and show that it satisfies a linear isoperimetric inequality. It then follows that F(2, n) is hyperbolic.