Knot floer homology detect unlink
Webcomputes the Floer homology of a specific Whitehead double of the .2;n/torus knot while[6]equates a particular knot Floer homology group of the 0–twisted Whitehead double with another invariant, the longitude Floer homology.Theorem 1.2is a signifi-cant improvement over either of these results and over any other results concerning the Floer ... WebLink homology theories Knot Floer homology detects the genus of a knot (Ozsváth–Szabó): g(K) = maxfa jHFKd (K;a) 6= 0g = minfa jHFKd (K;a) 6= 0g...and whether the knot is …
Knot floer homology detect unlink
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WebAdditionally we identify infinitely many pairs of links such that both links in the pair are each detected by link Floer homology but have the same Khovanov homology and knot Floer homology. Finally, we use some of our knot Floer detection results to give topological applications of annular Khovanov homology. WebApr 4, 2012 · A key ingredient of our proof is that the H_1/Torsion module structure on Heegaard Floer homology detects S^1xS^2 connected summands. No full-text available Citations (63) ... In this...
Webone knots have this property, for example (see Lemma 4). Our theorem follows from formulas which compute the Roer homology of manifolds obtained by Dehn surgery on a knot in terms of its knot Floer homology invariants [19], together with known properties of these latter invariants (e.g., they detect whether the knot is fibered [4, 14]). Webknot Floer homology detects the unknot [OS04a], trefoil knots [Ghi08, HW18], gure-eight knots ... cf. [BM20]. The novelty here is that the rank of the knot Floer homology alone is strong enough to detect the Hopf link. ... link is an unlink. Using the formula for the link Floer homology of split links given above, the relative rank ...
WebMar 16, 2024 · Ni has shown that the knot Floer homology H F K ^ of an oriented link L (in S 3 or more generally homology 3-spheres) detects χ ( L), the maximal Euler characteristic … WebNov 15, 2024 · I will also show that stronger detection results can be obtained as the knot Floer homology can be shown to detect T(2,8) and T(2,10), and that link Floer homology …
WebWhile the Alexander polynomial provides bounds on the knot genus and obstructions to fibering, knot Floer homology in fact detects both the knot genus and fibering. One particularly nice feature of the knot Floer complex is that it actually determines the Heegaard Floer homology of all rational surgeries along Kin Y.
WebFeb 11, 2011 · We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is … tommy\u0027s jim thorpe menuWebKnot Floer homology is known to detect the genus of a knot [10], as well as whether a knot is fibered [14]. There exists a refinement of HFK\ called link Floer homology [12], which detects the Thurston norm of the link complement [13]. tommy\u0027s dad on rugratsWebKhovanov homology of K2 to the Ozsv´ath-Szabo Floer homology of the branched dou-ble cover of K2. The Thurston norm of this latter manifold is non-trivial in the case when K is non-trivial. Since Ozsv´ath-Szab´o Floer homology detects the Thurston norm, this forces the rank of Floer homology, and hence the rank of Khovanov ho-mology, to grow. tomnjk02WebWe might wonder what aspect of a knot can detect if the knot is itself the unknot. In order to consider this, we introduce the concept of a Redemeister move. These can be seen in g. 5. Theorem 1. If two projections represent the same knot, then one can be ob-tained from the other using the Redemeister moves. Knot Floer homology is an invariant ... tomnafinogueWebHeegaard Floer homology, de ned by Ozsv ath-Szabo [OS04d], and knot Floer homology, de ned by Ozsv ath-Szab o [OS04b] and independently Rasmussen [Ras03], are invariants of 3-manifolds and knots inside of them. These notes aim to provide an overview of these invariants and the relationship between them. tomnjaryhttp://katlas.math.toronto.edu/wiki/Heegaard_Floer_Knot_Homology tommy\u0027s pizza tamarac plazaWebLagrangian Floer homology [6] in a suitable symmetric product of a Heegaard surface. Our aim here is to give a purely combinatorial presentation of knot Floer homology with coe cients in F for knots in the three-sphere. Our description can be extended to describe link Floer homology, and also it can be extended tomnlane\u0027s skin