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

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Abstract.

Let K=K(w,b,t) be a 1-bridge braid in a solid torus V, and let γ be a (p,q) curve on the torus T=∂V of the exterior M K of K. It will be shown that Dehn filling on T along γ 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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  1. Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA

    Ying-Qing Wu

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  1. Ying-Qing Wu
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Correspondence to Ying-Qing Wu.

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Mathematics Subject Classification (1991): 57N10

Partially supported by NSF grant DMS 0203394

Revised version: 28 November 2003

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Wu, YQ. The classification of Dehn fillings on the outer torus of a 1-bridge braid exterior which produce solid tori. Math. Ann. 330, 1–15 (2004). https://doi.org/10.1007/s00208-004-0519-0

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  • DOI: https://doi.org/10.1007/s00208-004-0519-0

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