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The length of unknotting tunnels

Daryl Cooper, Marc Lackenby and Jessica S Purcell
Algebraic & Geometric Topology 10 (2010) 637–661
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.

Keywords
unknotting tunnel, hyperbolic $3$–manifold, geodesic
Mathematical Subject Classification 2000
Primary: 57M50
References
Publication
Received: 11 August 2009
Accepted: 13 January 2010
Published: 13 March 2010
Authors
Daryl Cooper
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA 93106
USA
Marc Lackenby
Mathematical Institute
University of Oxford
24–29 St Giles’
Oxford OX1 3LB
United Kingdom
Jessica S Purcell
Department of Mathematics
Brigham Young University
Provo, UT 84604
USA