Abstract: Given a Riemann surface M, the Cheeger constant, h(M), is a geometric invariant which measures the extent to which M has ?bottlenecks? - a short, separating curve or collection of curves. We implement an algorithm of Benson to explicitly compute the Cheeger constant for a collection of arithmetic hyperbolic surfaces. The results have connections to arithmetic reflection groups, and to the relationship between the arithmetic and geometry of Fuchsian groups. This is joint work with Brian Benson.
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