Volume 13, issue 1 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Dehn surgery on knots of wrapping number $2$

Ying-Qing Wu

Algebraic & Geometric Topology 13 (2013) 479–503

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 K D 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.

Exceptional Dhen Surgery, hyperbolic manifolds, wrapping number
Mathematical Subject Classification 2010
Primary: 57N10
Received: 25 September 2011
Revised: 24 July 2012
Accepted: 4 October 2012
Published: 6 March 2013
Ying-Qing Wu
Department of Mathematics
The University of Iowa
14 MacLean Hall
Iowa City, IA 52242-1419