Geodesic
The length of unknotting tunnels
Cooper, Daryl1 ; Lackenby, Marc2 ; Purcell, Jessica S3
1Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
2Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford OX1 3LB, United Kingdom
3Department of Mathematics, Brigham Young University, Provo, UT 84604, USA
Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 637-661
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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.

DOI : 10.2140/agt.2010.10.637
Keywords: unknotting tunnel, hyperbolic $3$–manifold, geodesic

Cooper, Daryl  1   ; Lackenby, Marc  2   ; Purcell, Jessica S  3

1 Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
2 Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford OX1 3LB, United Kingdom
3 Department of Mathematics, Brigham Young University, Provo, UT 84604, USA 
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Cooper, Daryl; Lackenby, Marc; Purcell, Jessica S. The length of unknotting tunnels. Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 637-661. doi: 10.2140/agt.2010.10.637

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