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2013 The surgery unknotting number of Legendrian links
Bianca Boranda, Lisa Traynor, Shuning Yan
Involve 6(3): 273-299 (2013). DOI: 10.2140/involve.2013.6.273

Abstract

The surgery unknotting number of a Legendrian link is defined as the minimal number of particular oriented surgeries that are required to convert the link into a Legendrian unknot. Lower bounds for the surgery unknotting number are given in terms of classical invariants of the Legendrian link. The surgery unknotting number is calculated for every Legendrian link that is topologically a twist knot or a torus link and for every positive, Legendrian rational link. In addition, the surgery unknotting number is calculated for every Legendrian knot in the Legendrian knot atlas of Chongchitmate and Ng whose underlying smooth knot has crossing number 7 or less. In all these calculations, as long as the Legendrian link of j components is not topologically a slice knot, its surgery unknotting number is equal to the sum of j1 and twice the smooth 4-ball genus of the underlying smooth link.

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Bianca Boranda. Lisa Traynor. Shuning Yan. "The surgery unknotting number of Legendrian links." Involve 6 (3) 273 - 299, 2013. https://doi.org/10.2140/involve.2013.6.273

Information

Received: 7 May 2012; Revised: 20 May 2013; Accepted: 25 May 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 06227497
MathSciNet: MR3101761
Digital Object Identifier: 10.2140/involve.2013.6.273

Subjects:
Primary: 53D35 , 57R17
Secondary: 57M25

Keywords: genus , Lagrangian cobordism , Legendrian links , unknotting number

Rights: Copyright © 2013 Mathematical Sciences Publishers

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