Knot floer homotopy

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August undefined, 2024

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 … WebOur 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

[1706.07729] An overview of knot Floer homology - arXiv.org

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 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 … how to organise a cic

Connected Floer homology of covering involutions SpringerLink

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... 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. how to organise a charity dinner dance

A construction of knot Floer homotopy - ResearchGate

[math/0406402] On knot Floer homology and cabling - arXiv

WebApr 28, 2024 · Concordance questions of knots have been effectively studied by 4-dimensional topological methods by several authors. For a knot K in the three-sphere \(S^3\) one can consider the double branched cover \(\Sigma (K)\) of \(S^3\) branched along K.If K is a slice knot (i.e. it bounds a smoothly embedded disk in the 4-disk \(D^4\)) then … Webthe 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 ... how to order work cited links mlaWebpart 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 … how to organise a civil partnership

"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 mathtube.org

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... 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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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 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 …

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 … 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 …

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 ... 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.

WebWitten Floer theory [13, 11] and knot Floer homology [14]. Theorem 1.0.2 ﬁts in with this wider research program. The work of Manolescu and Sarkar [14] in on creating a …

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,... mw2 bright light bugWebKnot 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 ... how to organise a christeningWebthe 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 … how to organise a chess tournamentWebFloer Homotopy Theory August 22, 2024 to December 21, 2024 Organizers Mohammed Abouzaid (Columbia University), Andrew Blumberg (Columbia University), Kristen … how to organise a cleaning cupboardWebKnot Floer homology of Whitehead doubles 2281 Letting K denote the reﬂection of a knot K (ie in a given projection for K, K is obtained from K by changing each over-crossing to an … how to organise a conference eventWebOn 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 mw2 bright flashes fix todayWebFloer 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. mw2 calling card challenges