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arXiv · 0809.0183

Unknotting sequences for torus knots

Sebastian Baader
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Abstract

The unknotting number of a knot is bounded from below by its slice genus. It is a well-known fact that the genera and unknotting numbers of torus knots coincide. In this note we characterize quasipositive knots for which the genus bound is sharp: the slice genus of a quasipositive knot equals its unknotting number, if and only if the given knot appears in an unknotting sequence of a torus knot.

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Sebastian Baader. 2008-09-01. Unknotting sequences for torus knots. https://doi.org/10.1017/s0305004109990156

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