On iterated torus knots and transversal knots

William W Menasco

doi:10.2140/gt.2001.5.651

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On iterated torus knots and transversal knots

William W Menasco

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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.

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BibTeX RIS

William W Menasco. 2001-09-15. On iterated torus knots and transversal knots. https://doi.org/10.2140/gt.2001.5.651

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