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arXiv 2005.106532020-05-21math.GRmath.CO

Fibonacci群F（2，n）是双曲群，其中n为奇数且n ≥ 11

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

Christopher Chalk

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摘要：

本文证明了Fibonacci群F（2，n），当n为奇数且n >= 11时，是双曲的.我们这样做，通过应用曲率参数的任意van Kampen图F（2，n），并证明它满足线性等周不等式。因此，F（2，n）是双曲的。

英文摘要：

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.

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