On hyperbolic knots in S³ with exceptional surgeries at maximal distance

Audoux, B., Lecuona, A. G. and Roukema, F. (2018) On hyperbolic knots in S³ with exceptional surgeries at maximal distance. Algebraic and Geometric Topology, 18(4), pp. 2371-2417. (doi: 10.2140/agt.2018.18.2371)

Abstract

Baker showed that 1 0 of the 1 2 classes of Berge knots are obtained by surgery on the minimally twisted 5 –chain link. We enumerate all hyperbolic knots in S³ obtained by surgery on the minimally twisted 5 –chain link that realize the maximal known distances between slopes corresponding to exceptional (lens, lens), (lens, toroidal) and (lens, Seifert fibred) pairs. In light of Baker’s work, the classification in this paper conjecturally accounts for “most” hyperbolic knots in S³ realizing the maximal distance between these exceptional pairs. As a byproduct, we obtain that all examples that arise from the 5 –chain link actually arise from the magic manifold. The classification highlights additional examples not mentioned in Martelli and Petronio’s survey of the exceptional fillings on the magic manifold. Of particular interest is an example of a knot with two lens space surgeries that is not obtained by filling the Berge manifold (ie the exterior of the unique hyperbolic knot in a solid torus with two nontrivial surgeries producing solid tori).

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Garcia Lecuona, Professor Ana
• Authors: Audoux, B., Lecuona, A. G., and Roukema, F.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Algebraic and Geometric Topology
• Publisher: Mathematical Sciences Publishers
• ISSN: 1472-2747
• ISSN (Online): 1472-2739
• Copyright Holders: Copyright © 2018 Mathematical Sciences Publishers
• First Published: First published in Algebraic and Geometric Topology 18(4): 2371-2417
• Publisher Policy: Reproduced in accordance with the publisher copyright policy