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Bridge number and
integral Dehn surgery
Kenneth L Baker, Cameron Gordon and John Luecke |
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Algebraic & Geometric Topology 16 (2016) 1–40
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Abstract |
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In a –manifold , let be a knot and be an annulus which meets transversely. We define the notion of the pair being caught by a surface in the exterior of the link . For a caught pair , we consider the knot gotten by twisting times along and give a lower bound on the bridge number of with respect to Heegaard splittings of ; as a function of , the genus of the splitting, and the catching surface . As a result, the bridge number of tends to infinity with . In application, we look at a family of knots found by Teragaito that live in a small Seifert fiber space and where each admits a Dehn surgery giving . We show that the bridge number of with respect to any genus- Heegaard splitting of tends to infinity with . This contrasts with other work of the authors as well as with the conjectured picture for knots in lens spaces that admit Dehn surgeries giving . |
Keywords
Dehn surgery, bridge number, 3–manifolds, knot theory
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
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References |
Publication
Received: 20 December 2013
Revised: 11 February 2015
Accepted: 26 April 2015
Published: 23 February 2016
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Authors |
| Kenneth L Baker | |
| Department of Mathematics University of Miami 1365 Memorial Drive Coral Gables, FL 33146 USA |
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| Cameron Gordon | |
| Department of Mathematics University of Texas at Austin 2515 Speedway Stop C1200 Austin, TX 78712-1202 USA |
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| John Luecke | |
| Department of Mathematics University of Texas at Austin 2515 Speedway Stop C1200 Austin, TX 78712-0257 USA |
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