Geometry & Topology
- Geom. Topol.
- Volume 5, Number 2 (2001), 651-682.
On iterated torus knots and transversal knots
A knot type is exchange reducible if an arbitrary closed –braid representative of can be changed to a closed braid of minimum braid index by a finite sequence of braid isotopies, exchange moves and –destabilizations. In a preprint of Birman and Wrinkle, a transversal knot in the standard contact structure for is defined to be transversally simple if it is characterized up to transversal isotopy by its topological knot type and its self-linking number. Theorem 2 in the preprint establishes that exchange reducibility implies transversally simplicity. The main result in this note, establishes that iterated torus knots are exchange reducible. It then follows as a corollary that iterated torus knots are transversally simple.
Geom. Topol., Volume 5, Number 2 (2001), 651-682.
Received: 27 March 2001
Revised: 17 July 2001
Accepted: 15 August 2001
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M27: Invariants of knots and 3-manifolds 57N16: Geometric structures on manifolds [See also 57M50] 57R17: Symplectic and contact topology
Secondary: 37F20: Combinatorics and topology
Menasco, William W. On iterated torus knots and transversal knots. Geom. Topol. 5 (2001), no. 2, 651--682. doi:10.2140/gt.2001.5.651. https://projecteuclid.org/euclid.gt/1513883040