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Crossing number of
alternating knots in S
× I
Colin Adams, Thomas Fleming, Michael Levin and Ari M. Turner |
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Vol. 203 (2002), No. 1, 1–22
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Abstract |
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One of the Tait conjectures, which was stated 100 years ago and proved in the 1980’s, said that reduced alternating projections of alternating knots have the minimal number of crossings. We prove a generalization of this for knots in S × I, where S is a surface. We use a combination of geometric and polynomial techniques. |
Milestones
Received: 17 March 2000
Revised: 30 April 2001
Published: 1 March 2002
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Authors |
| Colin Adams | |
| Department of Mathematics Williams College Williamstown, MA 01267 |
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| Thomas Fleming | |
| Department of Mathematics University of California La Jolla, CA 92093 |
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| Michael Levin | |
| Department of Physics Massachusetts Institute of Technology Cambridge, MA 02139 |
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| Ari M. Turner | |
| Department of Physics Harvard University Cambridge, MA 02138 |
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