Knot contact homology

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August undefined, 2024

Web1. Knot contact homology: the idea The general setup for Legendrian contact homology is as follows: (1)Let Lbe a Legendrian submanifold of a contact manifold M. (This means … WebNov 16, 2024 · Knot contact homology and open Gromov-Witten theory Tobias Ekholm Knot 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.

KNOT CONTACT HOMOLOGY - etnyre.math.gatech.edu

WebAug 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 combinatorially. The improved invariant, which ... WebTome 4, 2024, p.661–780 DOI: 10.5802/jep.55 KNOT CONTACT HOMOLOGY, STRING TOPOLOGY, AND THE CORD ALGEBRA by Kai Cieliebak, Tobias Ekholm, Janko Latschev bussmann motor circuit protection table

Knot contact homology and open Gromov-Witten theory

WebLegendrian knots. The simplest case yields invariants of Legendrian knots inside contact three-manifolds.The relative contact homology has been shown to be a strictly more powerful invariant than the "classical invariants", namely Thurston-Bennequin number and rotation number (within a class of smooth knots).. Yuri Chekanov developed a purely … WebA few major discoveries in the late 20th century greatly rejuvenated knot theory and brought it further into the mainstream. In the late 1970s William Thurston 's hyperbolization theorem introduced the theory of hyperbolic 3-manifolds into knot theory and made it of prime importance. In 1982, Thurston received a Fields Medal, the highest honor ... WebOct 6, 2024 · In the past few years, there have been indications that knot contact homology and its higher genus generalizations are related via string theory to other knot invariants … bussman nnc

A complete knot invariant from contact homology

Title: Optimal enhanced dissipation and mixing for a time-periodic, Lipschitz … Comments: 167 pages; 23 figures; the second chapter of this paper … Knot contact homology, a topological link invariant of , is defined as the Legendrian … arXiv:1109.1542v2 [math.SG] 11 Jan 2012 KNOT CONTACT HOMOLOGY TOBIAS … 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. bussmann mcase fuseWebOn the symplectic / contact geometry side, we can study the Legendrian contact homology of the conormal legendrian to a knot. This invariant is pretty di cult to get our hands on, … ccbp training

"WebOct 7, 2016 · Perverse Sheaves and Knot Contact Homology. In this paper, which is mostly a research announcement, we give a new algebraic construction of knot contact homology in the sense of L. Ng [Ng05a]. For a link in , we define a differential graded (DG) -category with finitely many objects, whose quasi-equivalence class is a topological invariant of . " - Knot contact homology

Knot contact homology

WebOct 17, 2012 · Knot contact homology is a Floer-theoretic knot invariant derived from counting holomorphic curves in the cotangent bundle of \ (\mathbb {R}^ {3}\) with Lagrangian boundary condition on the... WebThis repository contains source code for the "Patterns in Knot-Floer homology" paper. The repository provides code for reproducing and modeling the data from the paper.

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WebAdvancing research. Creating connections. Webgeometric 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 …

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, … 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 ...

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 ... 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 …

WebJun 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 …

WebSep 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 … ccbp tech 4.0Weband knots; we call this the contact homology of the braid or knot. Although the homology of a DGA is generally hard to compute, there is a relatively simple form for the 0-dimensional part HC0 of the contact homology, and we can compute HC0 explicitly for a large number of knots. We concentrate on the invariant HC0 because it is diﬃcult in ... ccb-pwio17-s-05WebProposition 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. ccbp websiteWebMy Research and Language Selection Sign into My Research Create My Research Account English; Help and support. Support Center Find answers to questions about products, access, use, setup, and administration.; Contact Us Have a question, idea, or some feedback? We want to hear from you. ccbp static websiteWebAug 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 … bussmann mini circuit breakerWebfact 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]. bussmann motor protection chartWebKnot 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 … bussmann mpf2