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Characterizing slopes for torus knots

Ni, Yi and Zhang, Xingru (2014) Characterizing slopes for torus knots. Algebraic and Geometric Topology, 14 (3). 1249-1274 . ISSN 1472-2747. doi:10.2140/agt.2014.14.1249.

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A slope p/q is called a characterizing slope for a given knot K_0 in S^3 if whenever the p/q–surgery on a knot K in S^3 is homeomorphic to the p/q–surgery on K_0 via an orientation preserving homeomorphism, then K D K0 . In this paper we try to find characterizing slopes for torus knots T_(r,s). We show that any slope p/q which is larger than the number 30(r^(2)-1)(s^(2)-1)/67 is a characterizing slope for T_(r,s). The proof uses Heegaard Floer homology and Agol–Lackenby’s 6–theorem. In the case of T(5,2), we obtain more specific information about its set of characterizing slopes by applying further Heegaard Floer homology techniques.

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Additional Information:© 2014 Geometry & Topology Publications. First published in Algebraic & Geometric Topology in volume 14, number 3, published by Mathematical Sciences Publishers Received: 1 December 2012; Revised: 22 July 2013; Accepted: 29 July 2013; Published: 7 April 2014. The first author was partially supported by an AIM Five-Year Fellowship, NSF grant number DMS-1103976 and an Alfred P Sloan Research Fellowship. We are grateful to the organizers of the "Workshop on Topics in Dehn Surgery" at University of Texas at Austin for making our collaboration possible. We wish to thank John Baldwin for a conversation which made us realize a mistake in an earlier version of this paper.
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AIM Five-Year FellowshipUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20140618-104801586
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:46330
Deposited By: Jason Perez
Deposited On:19 Jun 2014 19:06
Last Modified:10 Nov 2021 17:24

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