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Knot contact homology

Webthe Legendrian contact homology DGA of the conormal lift of a knot K and also generalize the combinatorial description of knot contact homology to many-component links. Here the conormal lift of a link K is a union Λ K of Legendrian tori in the unit cotangent bundle S∗R3 of R3 with the contact structure given as the kernel of the canonical 1 ... WebKnot contact homology studies symplectic and contact geometric properties of conormals of knots in 3-manifolds using holomorphic curve techniques. It has connections to both mathematical and physical theories. On the mathematical side, we review the theory, show that it gives a complete knot invariant, and discuss its connections to Fukaya categories, …

Knot contact homology, string topology, and the cord algebra

Web2014 (English) In: Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, E-ISSN 1095-0753, Vol. 18, no 4, p. 827-956 Article in journal (Other academic) Published Abstract [en] We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. Webfact that knot contact homology recovers enough of the knot group (the fundamental group of the knot complement) to detect the unknot [Ng08] and torus knots, among others [GL]. greenford radio cars https://anchorhousealliance.org

Legendrian Contact Homology and Nondestabilizability

WebKnot contact homology is the homology of a differential graded algebra associated to a knot, the knot DGA (A,∂). By the general invariance result for Legendrian contact … WebApr 21, 2013 · 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-Witten disk amplitudes of a Lagrangian associated to a knot and augmentations of its contact homology algebra. WebSep 7, 2011 · The knot contact homology detects several classes of knots [5], and an enhancement of the knot contact homology is a complete invariant of knots [4]. ... The differential of (CY 1 (D 1 ), ∂ 1 ... greenford recycle booking

Embedded contact homology and applications - University of …

Category:[1606.07050] A complete knot invariant from contact …

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Knot contact homology

(PDF) Knot contact homology - ResearchGate

WebThe microlocal sheaf category is an invariant for the Legendrian knot conormal. The knot contact homology is another invariant of the Legendrian knot conormal, which uses the theory of theJ-holomorphic curves.

Knot contact homology

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WebSep 10, 2008 · Keywords: Heegaard Floer homology; Contact geometry; Legendrian knot 1. Introduction A contact structure, ξ, on a closed oriented three-manifold, Y , is an oriented two-dimensional sub-bundle of the tangent bundle, TY, which is completely non-integrable. This means there do not exist surfaces embedded in Y whose tangent planes lie in ξ in ... WebJun 22, 2016 · A complete knot invariant from contact homology Tobias Ekholm, Lenhard Ng, Vivek Shende We construct an enhanced version of knot contact homology, and show …

WebProposition 3.1. Let L be a Legendrian knot in the standard contact 3-sphere. If the characteristic algebra of L is nontrivial, then so is its contact homology. Proof. Suppose that the contact homology CH(L) = ker∂ im∂ of L is trivial. Then, since ∂(1) = 0, it must be the case that im∂ contains the unit element 1. WebKnot contact homology, a topological link invariant of K, is defined as the Legendrian homology of Λ K, the homology of a differential graded algebra generated by Reeb chords whose differential counts holomorphic disks in the symplectization R×U∗R3with Lagrangian boundary condition R×Λ K.

WebAug 20, 2011 · We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and produces a three-variable knot polynomial related to the A-polynomial.We provide a number of … WebApr 5, 2024 · The instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree,arising from the 2-dimensional ...

WebKnot contact homology An invariant of knots and links (Ng, Ekholm-Etnyre-Ng-Sullivan) A special case of Legendrian contact homology (Eliashberg, Chekanov, Eliashberg-Givental …

WebFirst of all, the knot contact homology describes knot invariants as invariants of the Legendrian submanifolds in the contact manifold. A knot is realized by an intersection of … flushing radiator 2006 pontiac grand prixWebAdvancing research. Creating connections. greenford recycling depotWebSep 7, 2011 · The knot contact homology detects several classes of knots [7], and an enhancement of the knot contact homology is a complete invariant of knots [6]. ... 2-knot … green ford quick lane greensboro ncWeb2 days ago · A knot in S^3 is topologically slice if it bounds a locally flat disk in B^4. A knot in S^3 is rationally slice if it bounds a smooth disk in a rational homology ball. We prove that the smooth concordance group of topologically and rationally slice knots admits a \mathbb {Z}^\infty subgroup. All previously known examples of knots that are both ... greenford recycling centerWebJun 16, 2024 · As an NSF Mathematical Sciences Postdoctoral Research Fellow at Rice University (2024-2024) and Swarthmore College (2024-2024), I made progress on a variety of projects in knot concordance, the study of 4-dimensional properties of knots and surfaces. More specifically, my work has focused on understanding the extent to which … flushing radiator 2010 toyota corollaWebgeometric side, passing from knot contact homology HC∗(K) to infinity transverse homology HT∞ ∗ (K) represents an extension of the base ring for the Legendrian contact … greenford recyclingWebAug 5, 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 … greenford refuse and recycling centre