Now showing items 1-9 of 9

• #### A complete knot invariant from contact homology ﻿

We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to ...
• #### A topological introduction to knot contact homology ﻿

(Bolyai Society Mathematical Studies, 2014-01-01)
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
• #### Augmentations are Sheaves ﻿

We show that the set of augmentations of the Chekanov-Eliashberg algebra of a Legendrian link underlies the structure of a unital A-infinity category. This differs from the non-unital category constructed in [BC], but is ...
• #### Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials ﻿

We sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large $N$ duality and Witten's connection between open Gromov-Witten invariants and Chern-Simons gauge theory, we ...
• #### Knot contact homology, string topology, and the cord algebra ﻿

(Journal de l’École polytechnique — Mathématiques, 2017)
The conormal Lagrangian LKof a knot K in R3is the submanifold of the cotangent bundle T∗R3consisting of covectors along K that annihilate tangent vectors to K. By intersecting with the unit cotangent bundle S∗R3, one obtains ...
• #### Legendrian contact homology in R^3 ﻿

This is an introduction to Legendrian contact homology and the Chekanov-Eliashberg differential graded algebra, with a focus on the setting of Legendrian knots in $\mathbb{R}^3$.
• #### Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold ﻿

(Journal of Differential Geometry, 2015-09)
We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in S1× S2or any connected sum #k(S1×S2), viewed as the contact boundary of the Weinstein manifold obtained by ...
• #### On the Stein framing number of a knot ﻿

For an integer $n$, write $X_n(K)$ for the 4-manifold obtained by attaching a 2-handle to the 4-ball along the knot $K\subset S^3$ with framing $n$. It is known that if $n< \overline{\text{tb}}(K)$, then $X_n(K)$ admits ...
• #### Representations, sheaves, and Legendrian $(2,m)$ torus links ﻿

We study an $A_\infty$ category associated to Legendrian links in $\mathbb{R}^3$ whose objects are $n$-dimensional representations of the Chekanov-Eliashberg differential graded algebra of the link. This representation category ...