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Finite Dehn surgeries on knots in S^3

Ni, Yi and Zhang, Xingru (2018) Finite Dehn surgeries on knots in S^3. Algebraic & Geometric Topology, 18 (1). pp. 441-492. ISSN 1472-2747. http://resolver.caltech.edu/CaltechAUTHORS:20180307-130606037

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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 4m and 4m + 4 are characterizing slopes for the torus knot T(2m + 1,2) for each m ≥ 1.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.2140/agt.2018.18.441DOIArticle
https://msp.org/agt/2018/18-1/p13.xhtmlPublisherArticle
https://arxiv.org/abs/1607.05685arXivDiscussion Paper
Alternate Title:Finite Dehn surgeries on knots in S3
Additional Information:© 2018 The Author(s). Received: 22 November 2016. Revised: 20 June 2017. Accepted: 14 September 2017. Published: 10 January 2018. Ni was partially supported by NSF grant numbers DMS-1103976, DMS-1252992, and an Alfred P Sloan Research Fellowship.
Funders:
Funding AgencyGrant Number
NSFDMS-1103976
NSFDMS-1252992
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:finite Dehn surgery, Culler-Shalen norm, Heegaard Floer homology
Classification Code:Mathematical Subject Classification 2010 Primary: 57M25
Record Number:CaltechAUTHORS:20180307-130606037
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180307-130606037
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85185
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:08 Mar 2018 00:14
Last Modified:08 Mar 2018 00:14

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