The length of unknotting tunnels
arXiv:0812.0858 · doi:10.2140/agt.2010.10.637
Abstract
We show there exist tunnel number one hyperbolic 3-manifolds with arbitrarily long unknotting tunnel. This provides a negative answer to an old question of Colin Adams.
20 pages, 6 figures. 20 pages, 6 figures. Daryl Cooper added as author. V2 contains two new sections, including a second proof of the main result, and a proof that the result holds for knots in homology spheres