Exceptional surgeries on alternating knots
Kazuhiro Ichihara, Hidetoshi Masai
TL;DR
This paper classifies all exceptional surgeries on hyperbolic alternating knots in the 3-sphere, completing the understanding of such surgeries for this class of knots and extending to certain Montesinos knots.
Contribution
It provides a complete classification of exceptional surgeries on hyperbolic alternating knots and extends results to specific Montesinos knots, finalizing the classification for arborescent knots.
Findings
Complete classification of exceptional surgeries on hyperbolic alternating knots.
Montesinos knots M (-1/2, 2/5, 1/(2q + 1)) with q ≥ 5 have no non-trivial exceptional surgeries.
Final step in classifying exceptional surgeries on arborescent knots.
Abstract
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 at least 5 have no non-trivial exceptional surgeries. This gives the final step in a complete classification of exceptional surgery on arborescent knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Geometry and complex manifolds