Toroidal Seifert fibered surgeries on Montesinos knots
Kazuhiro Ichihara, In Dae Jong
TL;DR
This paper proves that among Montesinos knots, only the trefoil admits a Dehn surgery resulting in a toroidal Seifert fibered 3-manifold, specifically at slope 0.
Contribution
It establishes a unique characterization of trefoil knots in the context of toroidal Seifert fibered surgeries among Montesinos knots.
Findings
Only the trefoil knot admits such a surgery.
The surgery slope for this case is 0.
No other Montesinos knots admit this type of surgery.
Abstract
We show that if a Montesinos knot admits a Dehn surgery yielding a toroidal Seifert fibered 3-manifold, then the knot is the trefoil knot and the surgery slope is 0.
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Taxonomy
TopicsGeometric and Algebraic Topology · Botulinum Toxin and Related Neurological Disorders · Homotopy and Cohomology in Algebraic Topology