2024 Knot homology

Knot homology

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August undefined, 2024

Web(See also: Tweaking JavaKh) The Khovanov Homology of a knot or a link , also known as Khovanov's categorification of the Jones polynomial of , was defined by Khovanov in [] … WebThe Heegaard-Floer Knot Homology program was written by Jean-Marie Droz in 2007 at the University of Zurich, based on methods of Anna Beliakova's arXiv:07050669. 8_19. in Arc …

History of knot theory - Wikipedia

WebIn its most basic form, knot Floer homology is an invariant for knots KˆS3, HFK([ K), which is a nite-dimensional bi-graded vector space over F = Z=2Z, i.e. HFK([ K) = M m;s HFK[ … apukauppa fi

Knot homology groups from instantons - Harvard University

Webhomology class [61,74], and whether such surfaces arise as ﬁbers in a ﬁbration of the 3-manifold over the circle [22,59,60]. In the present context, this amounts to the fact that knot Floer homology detects both the genus of a knot and whether it is ﬁbered. The detection theorems now follow from the paucity of genus one (and zero ... WebMODULE AND FILTERED KNOT HOMOLOGY THEORIES JEFF HICKS Abstract. We provide a new way to de ne Bar-Natan’s F 2[u] knot homology theory.The u torsion of BN ; is shown … WebInformally, we will think of a knot as a closed, elastic string in R3. Two knots are equivalent (isotopic) if one string can be deformed into the other without cutting the string. Our knots will carry an orientation, i.e. a forward direction indicated by an arrow. Knots are typically represented by planar diagrams called knot diagrams, as in ... apukapure

A combinatorial description of knot Floer homology - Annals …

On the skein exact squence for knot Floer homology

WebKnot Floer homology is very similar in structure to knot homologies coming from representation theory, such as those introduced by Khovanov [Kho00] and Khovanov … WebSep 20, 2007 · Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in S 3. We will prove this conjecture for null-homologous knots in arbitrary closed 3 … apukauppa tampereWebhomology [24] for closed oriented 3-manifolds. We will also discuss a related Floer homology invariant for knots in S3, [31], [34]. Let Y be an oriented closed 3-manifold. The simplest version of Heegaard Floer homology associates to Y a nitely generated Abelian PO was partially supported by NSF Grant Number DMS 0234311. apuke

"Webknot kthen Y = K ∪ (S1 ×D2), where ∂Kis identiﬁed with ∂(S1 × D2) by matching the meridian mwith the circle factor of S1 × D2 and the longitude ℓ with ∂D2. Note that H2(Y;Z/2) = … " - Knot homology

Knot homology

WebJun 14, 2004 · Abstract. In an earlier paper, we introduced a collection of graded Abelian groups HFK (Y,K) associated to knots in a three-manifold. The aim of the present paper is to investigate these groups for several specific families of knots, including the Kinoshita–Terasaka knots and their “Conway mutants”. These results show that HFK … WebAug 5, 2015 · ing the four-ball genus of torus knots. In Section 8 we give a description of Khovanov homology as the homology of a simpli-cial module by following our description of the cube category in this context. In Section 9 we discuss a quantum context for Khovanov homology that is obtained by building a Hilbert

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Web6. I will developp my comment here: Assume that Y is a closed 3 -manifold with rational sphere homology and let K be a null homologous knot in Y. Let ν ( K) be a neighborhood of K homeomorphic to a solid torus T = D 2 × S 1. I will denote by X … WebJun 16, 2024 · Branched covers bounding rational homology balls, joint with Paolo Aceto, Jeffrey Meier, Maggie Miller, JungHwan Park, and András Stipsicz, Algebraic & Geometric Topology 21 no. 7 (2024), pp 3569–3599. Amphichiral knots with large 4-genus, Bulletin of the London Mathematical Society 54 (2024), pp. 624-634. Last Modified: 06/16/2024

WebThe Floer homology group KHI.K/is supposed to be an “instanton” counterpart to the Heegaard knot homology of Ozsvath-Szab´ o and Ras-´ mussen [12,13]. It is known that the Euler characteristic of Heegaard knot homology gives the Alexander polynomial; so the above theorem can be taken WebThese homology theories have contributed to further mainstreaming of knot theory. In the last several decades of the 20th century, scientists and mathematicians began finding …

http://katlas.org/wiki/Khovanov_Homology WebNov 17, 2024 · Instanton knot homology was first introduced by Floer around 1990 and was revisited by Kronheimer and Mrowka around 2010. It is built based on the solution to a set of partial differential equations and is very difficult to compute. On the other hand, Heegaard diagrams are classical tools to describe knots and 3-manifolds combinatorially, and is …

WebThe discovery of the knot homology [Kho00] of the links in the three-sphere, motivated search for the homological invariants of the three-manifolds. Heegard-Floer homology …

WebSep 7, 2011 · Knot contact homology, a topological link invariant of , is defined as the Legendrian homology of , the homology of a differential graded algebra generated by … apuk gameshttp://katlas.math.toronto.edu/wiki/Heegaard_Floer_Knot_Homology apuke 2017http://katlas.math.toronto.edu/wiki/Heegaard_Floer_Knot_Homology apuk giirWebKnot Floer homology calculator. This is a companion for the papers Bordered knot algebras with matchings and Algebras with matchings and knot Floer homology by Peter Ozsváth and Zoltán Szabó. The program uses Planar Diagrams for knots. For example Trefoil = PD [X [4,2,5,1], X [2,6,3,5], X [6,4,1,3]] apu ke sath dhai saal question answerWebThe knot Floer homology is a signiﬁcant reﬁnement of the classical invariant. However, calculating the knot Floer homology is diﬃcult. In particular, computing the diﬀerentials involves counting points in certain moduli spaces of pseudoholo-morphic discs in a symplectic manifold. In [OS04c], Ozsvath and Szabo´ showed apu kebab caravacaWebBondage Basics Naughty Knots And Risque Restraint Naughty Knots - Dec 11 2024 Learn the ropes of erotic bondage with a discreet knot-tying guide featuring a playful ribbon- ... Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition ... apuk instagramWebMay 25, 2011 · Knot Homology from Refined Chern-Simons Theory Mina Aganagic, Shamil Shakirov We formulate a refinement of SU (N) Chern-Simons theory on a three-manifold via the refined topological string and the (2,0) theory on N M5 branes. The refined Chern-Simons theory is defined on any three-manifold with a semi-free circle action. apu kelowna