Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 18, Number 1 (2018), 441-492.
Finite Dehn surgeries on knots in $S^3$
Yi Ni and Xingru Zhang
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Abstract
We show that on a hyperbolic knot in , the distance between any two finite surgery slopes is at most , and consequently, there are at most three nontrivial finite surgeries. Moreover, in the case where admits three nontrivial finite surgeries, must be the pretzel knot . In the case where admits two noncyclic finite surgeries or two finite surgeries at distance , the two surgery slopes must be one of ten or seventeen specific pairs, respectively. For –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 and are characterizing slopes for the torus knot for each .
Article information
Source
Algebr. Geom. Topol., Volume 18, Number 1 (2018), 441-492.
Dates
Received: 22 November 2016
Revised: 20 June 2017
Accepted: 14 September 2017
First available in Project Euclid: 1 February 2018
Permanent link to this document
https://projecteuclid.org/euclid.agt/1517454222
Digital Object Identifier
doi:10.2140/agt.2018.18.441
Mathematical Reviews number (MathSciNet)
MR3748249
Zentralblatt MATH identifier
06828010
Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Keywords
finite Dehn surgery Culler-Shalen norm Heegaard Floer homology
Citation
Ni, Yi; Zhang, Xingru. Finite Dehn surgeries on knots in $S^3$. Algebr. Geom. Topol. 18 (2018), no. 1, 441--492. doi:10.2140/agt.2018.18.441. https://projecteuclid.org/euclid.agt/1517454222
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