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2017 Bounds on alternating surgery slopes
Duncan McCoy
Algebr. Geom. Topol. 17(5): 2603-2634 (2017). DOI: 10.2140/agt.2017.17.2603


We show that if pq–surgery on a nontrivial knot K yields the branched double cover of an alternating knot, then |pq| 4g(K) + 3. 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 Spq3(K) bounds a sharp 4–manifold X, then the intersection form of X takes the form of a changemaker lattice. We extend this to show that the intersection form is determined uniquely by the knot K, the slope pq and the Betti number b2(X).


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Duncan McCoy. "Bounds on alternating surgery slopes." Algebr. Geom. Topol. 17 (5) 2603 - 2634, 2017.


Received: 15 December 2014; Revised: 27 February 2017; Accepted: 25 March 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06791378
MathSciNet: MR3704237
Digital Object Identifier: 10.2140/agt.2017.17.2603

Primary: 57M12, 57M25
Secondary: 57M27

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.17 • No. 5 • 2017
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