On iterated torus knots and transversal knots
Abstract
A knot type is exchange reducible if an arbitrary closed n-braid representative can be changed to a closed braid of minimum braid index by a finite sequence of braid isotopies, exchange moves and +/- destabilizations. In the manuscript [J Birman and NC Wrinkle, On transversally simple knots, preprint (1999)] a transversal knot in the standard contact structure for S^3 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 of Birman and Wrinkle [op cit] 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- February 2000
- DOI:
- 10.48550/arXiv.math/0002110
- arXiv:
- arXiv:math/0002110
- Bibcode:
- 2000math......2110M
- Keywords:
-
- Mathematics - Geometric Topology;
- Mathematics - Dynamical Systems;
- 57M27;
- 57N16;
- 57R17;
- 37F20
- E-Print:
- Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper21.abs.html