Grid Diagrams, Braids, and Contact Geometry (2008)
We use grid diagrams to present a unified picture of braids, Legendrian knots, and transverse knots.
Rational Symplectic Field Theory for Legendrian knots (2008)
We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology,...
A family of transversely nonsimple knots (2008)
Khandhawit, Tirasan, Ng, Lenhard
We apply knot Floer homology to exhibit an infinite family of transversely nonsimple prime knots starting with $10_{132}$. We also discuss the combinatorial relationship between grid diagrams,...
A Skein Approach to Bennequin-Type Inequalities (2008)
We give a simple unified proof for several disparate bounds on Thurston–Bennequin number for Legendrian knots and self-linking number for transverse knots in , and provide a template for possible...
A skein approach to Bennequin type inequalities (2007)
We give a simple unified proof for several disparate bounds on Thurston-Bennequin number for Legendrian knots and self-linking number for transverse knots in R^3, and provide a template for possible...
Transverse Knots Distinguished by Knot Floer Homology (2007)
Ng, Lenhard, Ozsvath, Peter, Thurston, Dylan
We exhibit pairs of transverse knots with the same self-linking number that are not transversely isotopic, using the recently defined knot Floer homology invariant for transverse knots and some...
On arc index and maximal Thurston-Bennequin number (2006)
We discuss the relation between arc index, maximal Thurston--Bennequin number, and Khovanov homology for knots. As a consequence, we calculate the arc index and maximal Thurston--Bennequin number for...
A Legendrian Thurston-Bennequin bound from Khovanov homology (2005)
We establish an upper bound for the Thurston-Bennequin number of a Legendrian link using the Khovanov homology of the underlying topological link. This bound is sharp in particular for all...
Plane curves and contact geometry (2005)
We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous self-tangencies.
Conormal bundles, contact homology and knot invariants (2004)
We summarize recent work on a combinatorial knot invariant called knot contact homology. We also discuss the origins of this invariant in symplectic topology, via holomorphic curves and a conormal...
Legendrian solid-torus links (2004)
Differential graded algebra invariants are constructed for Legendrian links in the $1$-jet space of the circle. In parallel to the theory for $\R^3$, Poincar\'e--Chekanov polynomials and...
Legendrian solid-torus links (2004)
Differential graded algebra invariants are constructed for Legendrian links in the 1-jet space of the circle. In parallel to the theory for R^3, Poincare-Chekanov polynomials and characteristic...
Framed knot contact homology (2004)
We extend knot contact homology to a theory over the ring $\mathbb{Z}[\lambda^{\pm 1},\mu^{\pm 1}]$, with the invariant given topologically and combinatorially. The improved invariant, which is...
We present a topological interpretation of knot and braid contact homology in degree zero, in terms of cords and skein relations. This interpretation allows us to extend the knot invariant to...
Knot and braid invariants from contact homology I (2003)
We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The...