The length of unknotting tunnels

Cooper, Daryl; Lackenby, Marc; Purcell, Jessica S

doi:10.2140/agt.2010.10.637

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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

Volume 10, issue 2 (2010)