Vol. 6, No. 3, 2013

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The surgery unknotting number of Legendrian links

Bianca Boranda, Lisa Traynor and Shuning Yan

Vol. 6 (2013), No. 3, 273–299
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.

Keywords
Legendrian links, unknotting number, genus, Lagrangian cobordism
Mathematical Subject Classification 2010
Primary: 53D35, 57R17
Secondary: 57M25
Milestones
Received: 7 May 2012
Revised: 20 May 2013
Accepted: 25 May 2013
Published: 8 September 2013

Communicated by Kenneth S. Berenhaut
Authors
Bianca Boranda
Bryn Mawr College
Bryn Mawr, PA 19010
United States
Lisa Traynor
Department of Mathematics
Bryn Mawr College
Bryn Mawr, PA 19010
United States
Shuning Yan
Bryn Mawr College
Bryn Mawr, PA 19010
United States