2024 Knot homology

Knot homology

Author: vkfd

August undefined, 2024

http://homepages.math.uic.edu/~kauffman/IntroKhovanov.pdf WebUse the advanced features to specify the knots you want tabulated. Then select invariants and properties from the sections below. Click SUBMIT anywhere to produce your desired …

Floer homology - Wikipedia

WebJan 6, 2007 · Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to sl (2) and its standard representation. Our construction is related to that of Seidel-Smith by homological mirror symmetry. We show that the resulting doubly graded knot homology agrees with Khovanov homology. Webthe Markov moves for our homology as well as some explicit localization formulas for knot homology of a large class of links. 1. Introduction The 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 were the great horse hampden

[2304.06265] Topologically and rationally slice knots

WebFloer homology HFd functor of Ozsvath and Szabo´ [6]. In a similar vein, a very useful theory is the knot Floer homology HFK\(L) of Ozsvath-Szab´o and Rasmussen [7], [15]. In its simplest form, HFK\(L) is a bigraded vector space whose Euler characteristic is the Alexander polynomial. Knot Floer homology is known to detect the genus of a knot ... 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 … the awakenings review

[1510.01795] Lectures on knot homology - arXiv.org

Alexei Oblomkov

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 … Web2 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 ... the awakenings review magazineWebMay 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. the awakening statue chesterfield mo

"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 … " - Knot homology

Knot homology

A combinatorial description of knot Floer homology - Annals …

WebKnot Homology and sheaves on the Hilbert scheme of points on the plane (with L. Rozansky), Selecta Math. (N.S.) 24 (2024), no. 3, 2351--2454. Lectures on knot homology … 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 …

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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 ... 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 …

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 … 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.

WebJun 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). WebThe 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

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 …

There are several equivalent Floer homologies associated to closed three-manifolds. Each yields three types of homology groups, which fit into an exact triangle. A knot in a three-manifold induces a filtration on the chain complex of each theory, whose chain homotopy type is a knot invariant. (Their homologies satisfy similar formal properties to the combinatorially-defined Khovanov homology.) the great horse race the great hospital bishopgate norwichWeb(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 [] … the great hospitality parisWebJul 9, 2007 · P. Ozsváth, Z. Szabó. Published 9 July 2007. Mathematics. arXiv: Geometric Topology. The aim of this paper is to study the skein exact sequence for knot Floer homology. We prove precise graded version of this sequence, and also one using $\HFm$. Moreover, a complete argument is also given purely within the realm of grid diagrams. the great hospital nr1 4elWebknot 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) = … the great hotel escape tv showWebOct 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. the great hotel budapestWebMODULE 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 … the great houdini death