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Bounds on alternating
surgery slopes
Duncan McCoy |
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Algebraic & Geometric Topology 17 (2017) 2603–2634
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Abstract |
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We show that if –surgery on a nontrivial knot yields the branched double cover of an alternating knot, then . This generalises a bound for lens space surgeries first established by Rasmussen. We also show that all surgery coefficients yielding the double branched covers of alternating knots must be contained in an interval of width two and this full range can be realised only if the knot is a cable knot. The work of Greene and Gibbons shows that if bounds a sharp –manifold , then the intersection form of takes the form of a changemaker lattice. We extend this to show that the intersection form is determined uniquely by the knot , the slope and the Betti number . |
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Keywords
alternating knots, branched double covers, Dehn surgery
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Mathematical Subject Classification 2010
Primary: 57M12, 57M25
Secondary: 57M27
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References |
Publication
Received: 15 December 2014
Revised: 27 February 2017
Accepted: 25 March 2017
Published: 19 September 2017
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Authors |
| Duncan McCoy | |
| Department of Mathematics University of Texas Austin, TX United States |
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| http://www.ma.utexas.edu/users/d.mccoy/ | |
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