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

Abstract

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