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

Christopher P. Chalk 1
  • 1 University of East Anglia, Manchester, United Kingdom
Christopher P. Chalk


We prove that the Fibonacci group F(2,n) for 𝑛 odd and n11 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.

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The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.