We prove that the Fibonacci group for 𝑛 odd and is hyperbolic.
We do this by applying a curvature argument to an arbitrary van Kampen diagram of and show that it satisfies a linear isoperimetric inequality.
It then follows that is hyperbolic.
C. P. Chalk,
Fibonacci groups with aspherical presentations,
Comm. Algebra 26 (1998), 1511–1546.
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