Knot floer homotopy

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August undefined, 2024

Webpart 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 … WebGiven 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 …

APPLICATIONS OF INVOLUTIVE HEEGAARD FLOER HOMOLOGY

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. 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 … martyrs of the alamo 1915

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, … 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 … 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 … hunt electrical bungay

Knot Floer Homology and Categorification - Academic …

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. 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 ... huntelaar fifa 21 leagueWebFloer Homotopy Theory August 22, 2024 to December 21, 2024 Organizers Mohammed Abouzaid (Columbia University), Andrew Blumberg (Columbia University), Kristen … martyrs of tazacorte

"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 … " - Knot floer homotopy

Knot floer homotopy

Knot Floer homology and rational surgeries - Project Euclid

WebKnot Floer homology was originally de ned as a ltration on the chain complex of Heegaard Floer homology [39], a three-manifold invariant whose di erentials count holomorphic disks in a symmetric ... the diagram, and constructs a chain homotopy between the two complexes. These algebraic knot homologies were motivated by the concept of categori ... 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 …

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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 … 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.

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. WebFloer homology of a 3-manifold obtained by surgery on a given knot in terms of the Heegaard Floer homology data of the knot (see [4]). This makes Heegaard Floer homology an especially suitable tool for investigating the questions about Dehn surgery. Heegaard Floer homology is also very useful in bounding genera of various sur-faces.

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. WebAug 30, 2024 · A knot Floer stable homotopy type Authors: Ciprian Manolescu Stanford University Sucharit Sarkar Preprints and early-stage research may not have been peer …

WebAug 30, 2024 · A knot Floer stable homotopy type Authors: Ciprian Manolescu Stanford University Sucharit Sarkar Preprints and early-stage research may not have been peer reviewed yet. Abstract Given a grid...

WebOct 26, 2024 · Given a grid diagram for a knot or link K in S^3, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type … hunt electrical sandford ncWebSep 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 … hunt electrical upper huttWebNov 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 … martyrs of the civil rights movementWebFeb 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 … martyrs of the arenaWebJan 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 … martyrs movie online freeWebOn 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 hunt electric salt lakeWebrespectively 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 hunt electric supply greensboro