Communications in Analysis and Geometry

Volume 24 (2016)

Number 2

Exceptional surgeries on alternating knots

Pages: 337 – 377



Kazuhiro Ichihara (Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo, Japan)

Hidetoshi Masai (Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo, Japan)


We give a complete classification of exceptional surgeries on hyperbolic alternating knots in the $3$-sphere. As an appendix, we also show that the Montesinos knots $M(-1/2, \: 2/5, \: 1/(2q + 1))$ with $q \geq 5$ have no non-trivial exceptional surgeries. This gives the final step in a complete classification of exceptional surgeries on arborescent knots.


exceptional surgery, Seifert fibered surgery, alternating knot

2010 Mathematics Subject Classification

Primary 57M20. Secondary 57M25.

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Published 14 June 2016