TL;DR
This paper characterizes quasipositive knots for which the slice genus equals the unknotting number, showing they appear in unknotting sequences of torus knots, thus linking knot genus, unknotting number, and quasipositivity.
Contribution
It provides a complete characterization of quasipositive knots with sharp genus bounds, connecting unknotting sequences to torus knots.
Findings
Slice genus equals unknotting number for certain quasipositive knots.
Quasipositive knots in unknotting sequences of torus knots have sharp genus bounds.
The characterization links knot properties to unknotting sequences of torus knots.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.