Knot floer homotopy
WebThis 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 … 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
Knot floer homotopy
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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. 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.
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 …
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 … 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
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.)
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... buck shack wine near meWebin 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 buck shack wine ratingWebOn 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 buck shadesWebthe 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 ... buck shafferWebJan 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 … creek travelersWebKnot 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 … buckshaft road cinderfordWebWe 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 … buckshaft road