The surgery unknotting number of Legendrian links. (English) Zbl 1408.57013

Boranda, Bianca; Traynor, Lisa; Yan, Shuning

Involve 6, No. 3, 273-299 (2013).

Summary: 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 \(j-1\) and twice the smooth 4-ball genus of the underlying smooth link.

MSC:

57M27	Invariants of knots and \(3\)-manifolds (MSC2010)
53D35	Global theory of symplectic and contact manifolds
57R17	Symplectic and contact topology in high or arbitrary dimension

Keywords:

Legendrian links; unknotting number; genus; Lagrangian cobordism

Software:

KnotInfo