Geodesic
On iterated torus knots and transversal knots
Menasco, William W1
1 University at Buffalo, Buffalo, New York 14214, USA
Geometry & topology, Tome 5 (2001) no. 2, pp. 651-682.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

A knot type is exchange reducible if an arbitrary closed n–braid representative K of K can be changed to a closed braid of minimum braid index nmin(K) 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 S3 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.

DOI : 10.2140/gt.2001.5.651
Keywords: contact structures, braids, torus knots, cabling, exchange reducibility

Menasco, William W 1

1 University at Buffalo, Buffalo, New York 14214, USA 
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Menasco, William W. On iterated torus knots and transversal knots. Geometry & topology, Tome 5 (2001) no. 2, pp. 651-682. doi : 10.2140/gt.2001.5.651. http://geodesic.mathdoc.fr/articles/10.2140/gt.2001.5.651/

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