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Waist size for cusps in hyperbolic 3-manifolds II

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Abstract

The waist size of a cusp in an orientable hyperbolic 3-manifold is the length of the shortest nontrivial curve generated by a parabolic isometry in the maximal cusp boundary. Previously, it was shown that the smallest possible waist size, which is 1, is realized only by the cusp in the figure-eight knot complement. In this paper, it is proved that the next two smallest waist sizes are realized uniquely for the cusps in the \(5_2\) knot complement and the manifold obtained by (2,1)-surgery on the Whitehead link. One application is an improvement on the universal upper bound for the length of an unknotting tunnel in a 2-cusped hyperbolic 3-manifold.

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  1. Department of Mathematics and Statistics, Bascom Hall, Williams College, Williamstown, MA, 01267, USA

    Colin Adams

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  1. Colin Adams
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Correspondence to Colin Adams.

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Adams, C. Waist size for cusps in hyperbolic 3-manifolds II. Geom Dedicata 203, 53–66 (2019). https://doi.org/10.1007/s10711-019-00425-5

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  • DOI: https://doi.org/10.1007/s10711-019-00425-5

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