A Legendrian Thurston-Bennequin bound from Khovanov homology

By Lenhard L. Ng. 2005

74 citations recorded by the source corpus.

We establish an upper bound for the Thurston-Bennequin num- ber of a Legendrian link using the Khovanov homology of the underlying topological link. This bound is sharp in particular for all alternating links, and knots with nine or fewer crossings. AMS Classification 57M27; 57R17, 53D12

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/84bba8af0fd76155b0efdcb60762f162613711f6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Dan Rutherford
2. Dmitry Fuchs
3. Peter S. Ozsv'ath
4. Dylan Thurston

In Computational Theory and Mathematics

1. Lenhard L. Ng
2. Dylan Thurston
3. Tam'as K'alm'an
4. Peter S. Ozsv'ath
5. Dan Rutherford
6. K. Honda
7. Steven Sivek
8. T. Ekholm

In Geometry and Topology

1. Lenhard L. Ng
2. Tam'as K'alm'an
3. John B. Etnyre
4. Peter S. Ozsv'ath
5. T. Ekholm
6. Dylan Thurston
7. K. Honda
8. A. Stipsicz

Citations in the corpus

• Transverse knots distinguished by knot Floer homology (2007, background): “L1 is also a Legendrian representative of m(10132), the only topological knot with 10 or fewer crossings for which the maximal value of tb is currently unknown [21].”
• Legendrian knots and exact Lagrangian cobordisms (2012, background): “ordisms L1,...,L5 constructed in Section 8.1, we can assign an element of Kh(Λ). For each Li, the element ΨL i (1) coincides with Plamenevskaya’s transverse knot invariant [Pl], and also lies on Ng’s [Ng] line j −i = C, where C = {max(j −i) | Khi,j(L) 6= 0 }. By Remark 8.2, the exact Lagrangians Li ”
• Generating families and Legendrian contact homology in the standard contact space (2008, background): “diagram of a Legendrian isotopic Legendrian knot. For a front diagram L with a graded normal ruling τ, denote this complex as C(L,τ). Example. We consider a class of front diagrams first introduced in [Ng2] which always admit a normal ruling. Definition 4.1 A Mondrean diagram is a collection of horizo”
• Obstructions to Lagrangian concordance (2014, background): “Item (4) is the weak Khovanov bound tb(K) ≤ min-degqKhK(q, t/q) of [35].”