Knot floer homotopy

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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 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

Connected sums and involutive knot Floer homology

Webrelates the Heegaard Floer homology groups of three-manifolds obtained by surg-eries along a framed knot in a closed, oriented three-manifold. Before stating the result precisely, we review some aspects of Heegaard Floer homology brieﬂy, and then some of the topological constructions involved. 1.1. Background on Heegaard Floer groups: notation. 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… teri terry books

Floer homology - Wikipedia

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. 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.) 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 … teri teri new brunswick nj

APPLICATIONS OF INVOLUTIVE HEEGAARD FLOER HOMOLOGY

Knot Floer homology and rational surgeries - Project Euclid

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, … 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. tricare fertility coverage 2021WebOur 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 teri terry red sky burning

"WebWe use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to Stoffregen’s connected Seiberg–Witten Floer homology. " - Knot floer homotopy

Knot floer homotopy

A knot Floer stable homotopy type Request PDF - ResearchGate

WebJul 9, 2007 · An infinite family of knots with isomorphic knot Heegaard Floer homology with a nontrivial genus two mutant which shares the same total dimension in both knot Floer …

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WebOct 20, 2024 · The notion of homotopy ribbon concordance is a natural homotopy group analogue of the notion of smooth ribbon concordance initially introduced by Gordon [] for knots: we say the link J is smoothly ribbon concordant to the link L, written $J \ge _{{\text {sm}}} L$, if there is a smooth concordance from J to L such that the restriction of the … WebJun 21, 2004 · A precise formula for this relationship is presented. In fact, the homology groups in the top 2 filtration dimensions for the cabled knot are isomorphic to the original knot's Floer homology group in the top filtration dimension. The results are extended to (p,pn+-1) cables.

WebThis project began in the program entitled \Floer homotopy theory" held at MSRI/SL-Math on Aug-Dec in 2024. Thus this work was supported by the National Science Foundation under Grant No. DMS-1928930. The authors ... [86] , Knot Floer homology and integer surgeries, Algebraic & Geometric Topology 8 (2008), no. 1, 101{153. Webhomotopy classes of type-D morphisms from \CFD(S3 T) to Sis six-dimensional, generated over F 2 by f 1;f 2;f 3;g 1;g 2;g ... K-locally equivalent to the knot Floer complex of the twist knot 5 2, orequivalently,T#E. Proof. Itfollowsfromtheproofof[HKL16,LemmaA.1]thatwehave CFK UV(S3;D) ’CFK

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,... 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 …

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 homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry, but rather builds on the combinatorial definition of grid homology.

Web(Manolescu-Sarkar) A knot Floer stable homotopy type. ArXiv Given a grid diagram for a knot or link K in S3, we construct a spectrum whose homology is the knot Floer homology … teritex citiustech company addressWebKnot 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]. tricare fee schedule 2023 for providersWebpart is called knot Floer homology, and was independently constructed by Ozsv´ath-Szab´o and Rasmussen [OS04a, Ras03]. ... work. In [MP21], the author and Piccirillo produced homotopy 4-spheres from pairs of knots with the same 0-surgery. By computer experimentation, they found 5 examples of topologically slice knots such that, if any of … teritex office citiustechWebSep 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 … tricare fertilityWebWe 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 … tricare fee schedule lookupWebJan 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 … teritex knitting industries pvt. ltdWebin 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 tricare fee schedules 2021