Curvature distribution and hyperbolicity

Abstract

Abstract We describe a method, based on curvature distribution techniques on van Kampen diagrams, for proving finitely presented groups hyperbolic. We apply our method and show that the generalised Fibonacci group F ⁢ ( r , n ) F(r,n) is hyperbolic when r ≥ 3 r\geq 3 and n ≥ 6 ⁢ r + 1 n\geq 6r+1 and determine which of the groups F ⁢ ( 3 , n ) F(3,n) are hyperbolic.