Involve: A Journal of Mathematics

  • Involve
  • Volume 6, Number 3 (2013), 273-299.

The surgery unknotting number of Legendrian links

Bianca Boranda, Lisa Traynor, and Shuning Yan

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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.

Article information

Involve, Volume 6, Number 3 (2013), 273-299.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx] 57R17: Symplectic and contact topology
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Legendrian links unknotting number genus Lagrangian cobordism


Boranda, Bianca; Traynor, Lisa; Yan, Shuning. The surgery unknotting number of Legendrian links. Involve 6 (2013), no. 3, 273--299. doi:10.2140/involve.2013.6.273.

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