site stats

Knot homology

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 Presentation. The Heegaard-Floer Knot Homology is a categorification of the Alexander polynomial. Let us test that for the knot 8_19 : WebThis conjecture seems to hold true for torus knots and twist knots. However, I do not understand what the knot contact homology is. First of all, the knot contact homology …

[1211.6075] Lectures on Knot Homology and Quantum Curves

Webhomology [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. WebMar 7, 2024 · Download PDF Abstract: For a ribbon knot, it is a folk conjecture that the rank of its knot Floer homology must be 1 modulo 8, and another folk conjecture says the same about reduced Khovanov homology. We give the first counter-examples to both of these folk conjectures, but at the same time present compelling evidence for new conjectures that … broward county fl homes for sale https://prioryphotographyni.com

On the geography and botany of knot Floer homology - Springer

WebMay 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. WebMath 690: Knot Homologies. Overview: This course will be a brief introduction to homological invariants of knots and links, with an emphasis on the powerful invariant known as Khovanov homology and its applications to 3- and 4-dimensional topology. We'll start … 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 … broward county fl government

Instanton Floer homology and the Alexander polynomial

Category:Introduction

Tags:Knot homology

Knot homology

Knot homology groups from instantons - Harvard University

WebThis will take Khovanov homology as a central object of study, with a focus on the current state of homological invariants in low-dimensional topology, more generally, since … WebKnot 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]]

Knot homology

Did you know?

WebMar 24, 2024 · Classical knots in 3-space have no interesting homology. Instead, Alexander looked at the homology of their 2-fold covering spaces (an easy to see invariant that distinguishes a lot of knots). Reidemeister showed, shortly thereafter, that linking numbers in non-cyclic coverings (just a bit harder to see) fill in all the known gaps (as revealed ... WebJul 31, 2024 · For all rational t = m n ∈ [0, 2] the t-modified knot Floer homology tHFK (K), thought of as a graded F [v 1 / n]-module, is an invariant of the knot K. A homology class ξ is said to be homogeneous if it is represented by a cycle in a fixed grading. It is called non-torsion if v d ξ ≠ 0 for all d ∈ 1 n Z.

http://katlas.math.toronto.edu/wiki/Heegaard_Floer_Knot_Homology 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 applications of knot theory to problems in biology and chemistry. Knot theory can be used to determine if a molecule is chiral (has a "handedness") or not.

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 … http://katlas.org/wiki/Khovanov_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 …

http://homepages.math.uic.edu/~kauffman/IntroKhovanov.pdf ever by cotyWebDec 7, 2024 · Knot Homology and DAHA Seminar Fall 2024. Last Updated:December 07, 2024. The goal of this seminar is to understand part of the triangle of connections … broward county fl hurricane ianWebJun 19, 2024 · As for algebraic geometry, I have not seen much used in knot theory. If you go the homotopy theory route, you will need to know about sheaves, and eventually about schemes and stacks. A reasonable book would be Hartshorne (but only after the algebraic background above). ever by gail carson levineWebOct 7, 2015 · Lectures on knot homology. We provide various formulations of knot homology that are predicted by string dualities. In addition, we also explain the rich … broward county fl inmateWebOct 7, 2015 · We provide various formulations of knot homology that are predicted by string dualities. In addition, we also explain the rich algebraic structure of knot homology which can be understood in terms of geometric representation theory in these formulations. ever by meghan o\u0027rourkeWebThe 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 ever by gail carson levine summaryWebMODULE 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 … broward county fl marriage license