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2018 Finite Dehn surgeries on knots in $S^3$
Yi Ni, Xingru Zhang
Algebr. Geom. Topol. 18(1): 441-492 (2018). DOI: 10.2140/agt.2018.18.441

Abstract

We show that on a hyperbolic knot K in S 3 , the distance between any two finite surgery slopes is at most 2 , and consequently, there are at most three nontrivial finite surgeries. Moreover, in the case where K admits three nontrivial finite surgeries, K must be the pretzel knot P ( 2 , 3 , 7 ) . In the case where K admits two noncyclic finite surgeries or two finite surgeries at distance 2 , the two surgery slopes must be one of ten or seventeen specific pairs, respectively. For D –type finite surgeries, we improve a finiteness theorem due to Doig by giving an explicit bound on the possible resulting prism manifolds, and also prove that 4 m and 4 m + 4 are characterizing slopes for the torus knot T ( 2 m + 1 , 2 ) for each m 1 .

Citation

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Yi Ni. Xingru Zhang. "Finite Dehn surgeries on knots in $S^3$." Algebr. Geom. Topol. 18 (1) 441 - 492, 2018. https://doi.org/10.2140/agt.2018.18.441

Information

Received: 22 November 2016; Revised: 20 June 2017; Accepted: 14 September 2017; Published: 2018
First available in Project Euclid: 1 February 2018

zbMATH: 06828010
MathSciNet: MR3748249
Digital Object Identifier: 10.2140/agt.2018.18.441

Subjects:
Primary: 57M25

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 1 • 2018
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