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Levelling an unknotting
tunnel
Hiroshi Goda, Martin Scharlemann and Abigail Thompson |
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Geometry & Topology 4 (2000) 243–275
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arXiv: math.GT/9910099 |
Abstract |
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It is a consequence of theorems of Gordon-Reid [J. Knot Theory Ram. 4 (1995) 389–409] and Thompson [Topology 36 (1997) 505–507] that a tunnel number one knot, if put in thin position, will also be in bridge position. We show that in such a thin presentation, the tunnel can be made level so that it lies in a level sphere. This settles a question raised by Morimoto [Bull. Fac. Eng. Takushoku Univ. 3 (1992) 219–225], who showed that the (now known) classification of unknotting tunnels for 2–bridge knots would follow quickly if it were known that any unknotting tunnel can be made level. |
Keywords
tunnel, unknotting tunnel, bridge position, thin position,
Heegaard splitting
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Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27
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References |
Forward citations |
Publication
Received: 17 January 2000
Accepted: 18 September 2000
Published: 3 October 2000
Proposed: Cameron Gordon
Seconded: Robion Kirby, David Gabai
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Authors |
| Hiroshi Goda | |
| Graduate School of Science and
Technology Kobe University Rokko Kobe 657-8501 Japan |
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| Martin Scharlemann | |
| Mathematics Department University of California Santa Barbara California 93106 USA |
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| Abigail Thompson | |
| Mathematics Department University of California Davis CA 95616 USA |
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