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Obtaining genus $2$
Heegaard splittings from Dehn surgery
Kenneth L Baker, Cameron Gordon and John Luecke |
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Algebraic & Geometric Topology 13 (2013) 2471–2634
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Abstract |
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Let be a hyperbolic knot in and suppose that some Dehn surgery on with distance at least from the meridian yields a –manifold of Heegaard genus . We show that if does not contain an embedded Dyck’s surface (the closed nonorientable surface of Euler characteristic ), then the knot dual to the surgery is either –bridge or –bridge with respect to a genus Heegaard splitting of . In the case that does contain an embedded Dyck’s surface, we obtain similar results. As a corollary, if does not contain an incompressible genus surface, then the tunnel number of is at most . |
Keywords
Dehn surgery, bridge number, Heegaard splitting
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Mathematical Subject Classification 2010
Primary: 57M27
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References |
Publication
Received: 1 May 2012
Revised: 6 February 2013
Accepted: 7 March 2013
Published: 5 July 2013
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Authors |
| Kenneth L Baker | |
| Department of Mathematics University of Miami PO Box 249085 Coral Gables, FL 33146 USA |
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| http://math.miami.edu/~kenken | |
| Cameron Gordon | |
| Department of Mathematics University of Texas at Austin 1 University Station C1200 Austin, TX 78712-1202 USA |
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| http://www.ma.utexas.edu/text/webpages/gordon.html | |
| John Luecke | |
| Department of Mathematics The University of Texas at Austin 1 University Station C1200 Austin, TX 78712-0257 USA |
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