2024 Knot floer homotopy

Knot floer homotopy

Author: ownp

August undefined, 2024

WebOn the one hand, singular instanton Floer homology is more directly related to the fundamental group of the knot complement. For example, this Floer homology can be used to show that the knot group of any non-trivial knot admits a non-abelian representation into the Lie group SUp2q[KM04,KM10b]. On the other hand, knot Floer homology currently WebJan 15, 2009 · This space is well-defined, its homology is the grid homology, and its stable homotopy type is a knot invariant. Thus to each knot, we can associate an invariant spectrum, whose F_2 homology...

Floer homology - Wikipedia

Web3.A knot Floer stable homotopy type (with S. Sarkar), preprint (2024), arXiv:2108.13566 ... 23.An introduction to knot Floer homology, in Physics and mathematics of link homology, Contemp. Math. 680, AMS (2016), 99–135 24.Cornered Heegaard Floer homology (with C. Douglas and R. Lipshitz), Memoirs of the American Webproved that if a hyperbolic knot K⊂ S3 has the same knot Floer homology as the torus knot T(5,2), then the monodromy of Kis freely isotopic to a pseudo-Anosov map without ﬁxed … all grave locations

Homotopy ribbon concordance and Alexander polynomials

Webrespectively knots, in Section 2, respectively Section 3, whose chain homotopy type (and in particular, homology) is independent of the choice of Heegaard diagram. Moreover, from the knot invariant associated to a knot Kin S3, one can compute the 3-manifold invariant for any Dehn surgery along K; we discuss this relationship WebApr 13, 2024 · The involutiv e knot Floer homology package associates to a knot K a well-deﬁned element in I U. ... up to homotopy due to the lack of naturalit y in bordered Floer homology, it is still a ... all gravel

$arXiv:1411.1275v1 [math.GT] 5 Nov 2014$

InvarianceofKnotLatticeHomologyand Homotopy

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.) WebFloer Homotopy Theory August 22, 2024 to December 21, 2024 Organizers Mohammed Abouzaid (Columbia University), Andrew Blumberg (Columbia University), Kristen … all grateful dead albumsWebholomorphic disks and knot invariants peter ozsvath and zolt´ an szab´ o´ ... all gravy gif

"WebHeegaard Floer homology is an invariant of 3-manifolds, and knots and links within them, introduced by P. Oszváth and Z. Szabó in the early 2000s. Because of its relative … " - Knot floer homotopy

Knot floer homotopy

Knot Floer homology detects fibred knots SpringerLink

WebNov 1, 2011 · Let K be a rationally null-homologous knot in a three-manifold Y.We construct a version of knot Floer homology in this context, including a description of the Floer homology of a three-manifold obtained as Morse surgery on the knot K.As an application, we express the Heegaard Floer homology of rational surgeries on Y along a null-homologous … WebWe define a new smooth concordance homomorphism based on the knot Floer complex and an associated concordance invariant, . As an application, we show that an infinite family of topologically slice knots are independent…

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WebFeb 15, 2024 · Given a grid diagram for a knot or link K in the three-sphere, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the … Webin 1999, there has been a lot of progress in categori cation of knot polynomials, and investigation on knot homology theories in general. In 2004, Bar-Natan published [Bar04] a description of the Khovanov Bracket, [[L]] as a homotopy category over the cobordisms. Thie gave an explicit way to produce new homology

Webthe filtered chain homotopy type of CFK tells you about the Heegaard Floer homology of various surgeries on K; the highest a for which HFK * (S 3 ,K,a) is nonzero is the Seifert … WebWe introduce a contact invariant in the bordered sutured Heegaard Floer homology of a three-manifold with boundary. The input for the invariant is a contact manifold $(M, \xi , \mathcal {F})$ whose convex boundary is equipped with a signed singular foliation $\mathcal {F}$ closely related to the characteristic foliation. Such a manifold admits a …

WebAbstract: Heegaard Floer homology is an invariant of 3-manifolds, and knots and links within them, introduced by P. Oszváth and Z. Szabó in the early 2000s. Because of its relative computability by the standards of gauge and Floer theoretic invariants, it has enjoyed considerably popularity. WebOct 27, 2024 · The main goal of the project is the following: To every knot, three-dimensional shape, or symplectic shape, one should associate a different object, called a Floer space or a Floer homotopy type, whose (ordinary) homology is the Floer homology of the initial shape. This has been accomplished so far in a limited number of cases.

WebNov 1, 2011 · As an application, we express the Heegaard Floer homology of rational surgeries on Y along a null-homologous knot K in terms of the filtered homotopy type of …

WebThis is a survey article about knot Floer homology. We present three constructions of this invariant: the original one using holomorphic disks, a combinatorial description using grid diagrams,... all grave locations rdr2WebOur goal is to review some recent applications of Heegaard Floer theory to ho- mology cobordism and knot concordance, and to discuss the power and limitations of these tools to address major open questions in the eld. 1.1. Homology cobordism. Two closed, oriented 3-manifolds Y 0;Y all graves ices staffWebJan 15, 2009 · Given a knot presented in a grid diagram, we associate to it a partially ordered set with certain properties, and then construct a CW complex whose cells correspond to … all gravy memeWebThis 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]] The X and the extra brackets are optional, the program will look for the PD start and then read … all gray color codeWebGiven a grid diagram for a knot or link K in the three-sphere, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type of the … all gravyWebthe knot. From the perspective of knot Floer homology, (1,1) knots are particularly appeal-ing. It was ﬁrst observed by Goda et al. [5]that(1,1) knots are exactly those knots that can be presented by a doubly pointed Heegaard diagram of genus one. The chain com-plex for knot Floer homology is deﬁned in terms of a doubly pointed Heegaard ... all gratin potatoes recipeWebKnot Floer homology is a re nement of Heegaard Floer homology for knots embedded in 3- manifolds, introduced by Ozsv ath and Szab o [OS04a] and independently by Rasmussen [Ras03]. Link Floer homology is a generalization of knot Floer homology for links in 3-manifolds, developed by Ozsv ath and Szab o [OS08]. all grayscale funds