Now showing items 1-11 of 11

• 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.
• Knot contact homology ﻿

(Geometry & Topology, 2013-04-30)
The conormal lift of a link K in ℝ3is a Legendrian submanifold ∧Kin the unit cotangent bundle U*ℝ3of ℝ3with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link invariant ...
• 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 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 ARC INDEX AND MAXIMAL THURSTON–BENNEQUIN NUMBER ﻿

(Journal of Knot Theory and Its Ramifications, 2012-04)
We discuss the relation between arc index, maximal ThurstonBennequin number, and Khovanov homology for knots. As a consequence, we calculate the arc index and maximal ThurstonBennequin number for all knots with at most 11 ...
• On transverse invariants from Khovanov homology ﻿

(Quantum Topology, 2015)
© European Mathematical Society. In [31], O. Plamenevskaya associated to each transverse knot K an element of the Khovanov homology of K. In this paper, we give two re_nements of Plamenevskaya’s invariant, one valued in ...
• 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 ...
• Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra ﻿

(Algebraic & Geometric Topology, 2013-08-01)
We develop a close relation between satellites of Legendrian knots in ℝ3and the Chekanov-Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence between rulings of a ...
• The cardinality of the augmentation category of a Legendrian link ﻿

(Mathematical Research Letters, 2017)
We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R3. This ℓhomotopy cardinality' is an invariant of the category and allows for a weighted count ...
• Topological strings, D-model, and knot contact homology ﻿

(Advances in Theoretical and Mathematical Physics, 2014)
© 2014 International Press. We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. In particular, we establish the proposed relation between the Gromov- ...