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Dehn filling and the geometry of unknotting tunnels
Cooper, D Futer, D Purcell, JS
Cooper, D
Futer, D
Purcell, JS
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Journal Article
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2013-07-18
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10.2140/gt.2013.17.1815
Abstract
Any one-cusped hyperbolic manifold M with an unknotting tunnel x is obtained by Dehn filling a cusp of a two-cusped hyperbolic manifold. In the case where M is obtained by "generic" Dehn filling, we prove that r is isotopic to a geodesic, and characterize whether r is isotopic to an edge in the canonical decomposition of M. We also give explicit estimates (with additive error only) on the length of r relative to a maximal cusp. These results give generic answers to three long-standing questions posed by Adams, Sakuma and Weeks. We also construct an explicit sequence of one-tunnel knots in S3, all of whose unknotting tunnels have length approaching infinity.
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Mathematical Sciences Publishers
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Geometry and Topology
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