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Geometriae Dedicata

, Volume 203, Issue 1, pp 53–66 | Cite as

Waist size for cusps in hyperbolic 3-manifolds II

  • Colin AdamsEmail author
Original Paper
  • 53 Downloads

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.

Keywords

Hyperbolic 3-manifold Waist size Cusp 

Mathematics Subject Classification (2010)

57M50 

Notes

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Bascom HallWilliams CollegeWilliamstownUSA

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