WebJan 9, 2024 · Link Floer homology is a powerful inv ariant of links in S3 due to Ozsv´ ath-Szab´ o, taking value in the category of m ulti-graded vector spaces [31]. In this paper we address several varian... WebIn Section 2.5, we define knot Floer homology and state some of its properties. Finally, in Section 2.6, we discuss holomorphic triangles, cobordisms, and induced maps on Heegaard Floer homology. One important property of Heegaard Floer homology is that one can compute it for sufficiently large knot surgeries using knot Floer homology.

Knot Floer homology detects fibred knots - ResearchGate

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 … WebJul 1, 2009 · We also prove a knot Floer homology analog of arXiv:1910.04246v1 [math.GT] and give a partial answer to when the equality holds in the rank inequality between the … ignition union hook

Knot Floer homology detects genus-one fibred knots - ResearchGate

WebAug 5, 2024 · We prove that knot Floer homology and Khovanov homology can detect non-fibered knots, including the knot , and that HOMFLY homology detects infinitely many … 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]). ignition unit type t1d11-01a