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Unknotting sequences for torus knots

Published online by Cambridge University Press:  06 July 2009

SEBASTIAN BAADER
SEBASTIAN BAADER*
Affiliation:
Department of Mathematics, ETH Zürich, Switzerland. e-mail: sebastian.baader@math.ethz.ch
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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 paper 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 1 , January 2010 , pp. 111 - 116
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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