The Classification of Dehn fillings on the outer torus of a 1-bridge braid exterior which produce solid tori

Details The Classification of Dehn fillings on the outer torus of a 1-bridge braid exterior which produce solid tori The Classification of Dehn fillings on the outer torus of a 1-bridge braid exterior which produce solid tori

2006-10-27

arxiv.org/abs/math/0610868v1

Math. Ann. 330 (2004), 1--15

Mathematics

Geometric Topology

Scientific paper

Let $K= K(w,b,t)$ be a 1-bridge braid in a solid torus $V$, and let $\gamma$ be a $(p,q)$ curve on the torus $T = \partial V$ of the exterior $M_K$ of $K$. It will be shown that Dehn filling on $T$ along $\gamma$ produces a solid torus if and only if $p$ and $q$ satisfy one of four conditions determined by the parameters $(w,b,t)$ of the knot $K$. This solves the classification problem raised by Menasco and Zhang for such Dehn fillings.

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