Related papers: Knot contact homology

The main result of this paper is that, off of a `fundamental class' in degree 1, the linearized Legendrian contact homology obeys a version of Poincare duality between homology groups in degrees k and -k. Not only does the result itself…

We propose a gauge model of quantum electrodynamics (QED) and its nonabelian generalization from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from…

We define a bigraded homology theory whose Euler characteristic is the quantum sl(3) link invariant.

Using the combinatorial approach to knot Floer homology, we define an invariant for Legendrian knots in the three-sphere, which takes values in link Floer homology. This invariant can be used to also construct an invariant of transverse…

A Fox p-colored knot $K$ in $S^3$ gives rise to a $p$-fold branched cover $M$ of $S^3$ along $K$. The pre-image of the knot $K$ under the covering map is a $\dfrac{p+1}{2}$-component link $L$ in $M$, and the set of pairwise linking numbers…

It had been known since old times [MO, Da] that there exists a universal finite type invariant ("an expansion") Z^{old} for Knotted Trivalent Graphs (KTGs), and that it can be chosen to intertwine between some of the standard operations on…

Let $K\subset S^3$ be a knot and $\eta, \gamma \subset S^3\backslash K$ be simple closed curves. Denote by $\Sigma_q(K)$ the $q$-fold cyclic branched cover of $K$. We give an explicit formula for computing the linking numbers between lifts…

Given a knot K in S^3, Seidel and Smith described in arXiv:1002.2648v3 a graded cohomology group Kh_{symp,inv}(K), a variant of their symplectic Khovanov cohomology group. They also constructed a spectral sequence converging to the Heegaard…

Using the covering involution on the double branched cover of the three-sphere branched along a knot, and adapting ideas of Hendricks-Manolescu and Hendricks-Hom-Lidman, we define new knot invariants and apply them to deduce novel linear…

We give a new definition of the knot invariant associated to the Lie algebra su_{N+1}. The knot or link must be presented as the plat closure of a braid. The invariant is then a homological intersection pairing between two submanifolds of a…

We study the natural inclusion of the space of Legendrian embeddings in $(\mathbb{S}^3,\xi_{\operatorname{std}})$ into the space of smooth embeddings from a homotopical viewpoint. T. K\'alm\'an posed in [Kal] the open question of whether…

In this note, we observe that the hat version of the Heegaard Floer invariant of Legendrian knots in contact three-manifolds defined by Lisca-Ozsvath-Stipsicz-Szabo can be combinatorially computed. We rely on Plamenevskaya's combinatorial…

A homological invariant of 3-manifolds is defined, using abelian Yang-Mills gauge theory. It is shown that the construction, in an appropriate sense, is functorial with respect to the families of 4-dimensional cobordisms. This construction…

We compute the Chekanov-Eliashberg contact homology of what we call the Legendrian closure of a positive braid. We also construct an augmentation for each such link diagram. Then we apply the monodromy techniques established in an earlier…

We study the structure underlying Ng's conjecture, which relates the degree $0$ abelian knot contact homology of a knot $K$ to the coordinate ring of the $SL_2(\mathbf{C})$-character variety $X(\Sigma_2 K)$ of the $2$-fold branched cover of…

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invariants have come to play a central role in describing matter,…

Ozsvath and Szabo defined an analog of the Froyshov invariant in the form of a correction term for the grading in Heegaard Floer homology. Applying this to the double cover of the 3-sphere branched over a knot K, we obtain an invariant…

Given a grid diagram for a knot or link K in $S^3$, we construct a filtered spectrum whose homology is the knot Floer homology of K. We conjecture that the filtered homotopy type of the spectrum is an invariant of K. Our construction does…

Using convex surfaces and Kanda's classification theorem, we classify Legendrian isotopy classes of Legendrian linear curves in all tight contact structures on $T^3$. Some of the knot types considered in this article provide new examples of…

We define and study a bigraded knot invariant whose Euler characteristic is the Alexander polynomial, closely connected to knot Floer homology. The invariant is the homology of a chain complex whose generators correspond to Kauffman states…