Dehn surgery on knots of wrapping number 2

作者：Wu Ying Qing^*

来源：Algebraic and Geometric Topology, 2013, 13(1): 479-503.

DOI：10.2140/agt.2013.13.479

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 boolean OR D is incompressible in the knot exterior, then K admits at most one exceptional surgery, which must be toroidal. Embedding V in S-3 gives infinitely many knots K-n with a slope r(n) corresponding to a slope r of K in V. If r surgery on K in V is toroidal then either K-n(r(n)) 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.

• 出版日期2013