Dehn filling and the geometry of unknotting tunnels

Details Dehn filling and the geometry of unknotting tunnels Dehn filling and the geometry of unknotting tunnels

2011-05-17

arxiv.org/abs/1105.3461v1

Mathematics

Geometric Topology

45 pages, 17 figures

Scientific paper

Let M be a one-cusped hyperbolic manifold, and tau an unknotting tunnel for M. In the case where M is obtained by "generic" Dehn filling on one cusp of a two-cusped hyperbolic manifold, we prove that tau is isotopic to a geodesic, and characterize whether tau is isotopic to an edge in the canonical decomposition of M. We also give explicit estimates (with additive error only) on the length of tau 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 S^3, all of whose unknotting tunnels have length approaching infinity.

Affiliated with

Also associated with

No associations

Rating

Dehn filling and the geometry of unknotting tunnels does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dehn filling and the geometry of unknotting tunnels, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dehn filling and the geometry of unknotting tunnels will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727992