Knot floer homotopy

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August undefined, 2024

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 … WebFloer Homotopy Theory August 22, 2024 to December 21, 2024 Organizers Mohammed Abouzaid (Columbia University), Andrew Blumberg (Columbia University), Kristen …

The knot Floer complex and the smooth concordance group

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 … 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 sonet microsystems

arXiv:math/0209056v1 [math.GT] 6 Sep 2002

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 … 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. 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 … small dog bathroom schedule

Homotopy ribbon concordance and Alexander polynomials

A knot Floer stable homotopy type Mathematics

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. 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,... soneto 35 shakespeareWebWe 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 … small dog beds at walmart

"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. " - Knot floer homotopy

Knot floer homotopy

WebJan 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 …

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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 … 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 …

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 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…

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, … 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...

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 ...

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. so-net mail passwordWebNov 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 … small dog bathing stationWebHeegaard 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 … small dog bathWebOct 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 … small dog bed with removable coverWebFeb 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. small dog bandanas with bowsWebApr 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 … small dog big couchWebthe 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 ... small dog beds washable