Translator Disclaimer
2013 Dehn surgery on knots of wrapping number $2$
Ying-Qing Wu
Algebr. Geom. Topol. 13(1): 479-503 (2013). DOI: 10.2140/agt.2013.13.479

Abstract

Suppose K is a hyperbolic knot in a solid torus V intersecting a meridian disk D twice. We will show that if K is not the Whitehead knot and the frontier of a regular neighborhood of KD is incompressible in the knot exterior, then K admits at most one exceptional surgery, which must be toroidal. Embedding V in S3 gives infinitely many knots Kn with a slope rn corresponding to a slope r of K in V. If r surgery on K in V is toroidal then either Kn(rn) are toroidal for all but at most three n, or they are all atoroidal and nonhyperbolic. These will be used to classify exceptional surgeries on wrapped Montesinos knots in a solid torus, obtained by connecting the top endpoints of a Montesinos tangle to the bottom endpoints by two arcs wrapping around the solid torus.

Citation

Download Citation

Ying-Qing Wu. "Dehn surgery on knots of wrapping number $2$." Algebr. Geom. Topol. 13 (1) 479 - 503, 2013. https://doi.org/10.2140/agt.2013.13.479

Information

Received: 25 September 2011; Revised: 24 July 2012; Accepted: 4 October 2012; Published: 2013
First available in Project Euclid: 19 December 2017

zbMATH: 1262.57022
MathSciNet: MR3031649
Digital Object Identifier: 10.2140/agt.2013.13.479

Subjects:
Primary: 57N10

Rights: Copyright © 2013 Mathematical Sciences Publishers

JOURNAL ARTICLE
25 PAGES


SHARE
Vol.13 • No. 1 • 2013
MSP
Back to Top