Abstract
AbstractThe 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.
Publisher
Cambridge University Press (CUP)
Reference14 articles.
1. Le problème de J. Milnor sur le nombre gordien des nœuds algébriques;Boileau;Enseign. Math.,1984
2. Slice and Gordian numbers of track knots;Baader;Osaka J. Math.,2005
3. [10] Rolfsen D. Knots and Links (Publish or Perish, 1976).
4. Quasipositivity as an obstruction to sliceness
5. Quasi-positivité d'une courbe analytique dans une boule pseudo-convexe
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