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
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