Knot floer homology detect unlink

Author: rkww

August undefined, 2024

http://katlas.math.toronto.edu/wiki/Heegaard_Floer_Knot_Homology WebThe aim of this paper is to give an introduction to Heegaard Floer homology [24] for closed oriented 3-manifolds. We will also discuss a related Floer homology invariant for knots in S3, [31], [34]. Let Y be an oriented closed 3-manifold. The simplest version of Heegaard Floer homology associates to Y a nitely generated Abelian

Knot Floer homology of Whitehead doubles - Project Euclid

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 … WebThe instanton Floer homology of a knot in S3 is a vector space with a canonical mod 2grading. It carries a distinguished endomorphism of even degree, arising from the 2-dimensional homology class represented by a Seifert surface. The Floer homology decomposes as a direct sum of the generalized eigenspaces of this en-domorphism. christmas tree metal tiered tray

Instanton Floer homology and the Alexander polynomial

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. 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... WebWe give new link detection results for knot and link Floer homology inspired by recent work on Khovanov homology. We show that knot Floer homology detects $T(2,4)$, $T(2,6)$, … get password off iphone

A combinatorial description of knot Floer homology - Annals …

Knot Floer homology detects fibred knots - ResearchGate

WebFloer homology can detect the trefoil knot and the ﬁgure 8 knot; see Ghiggini[14]. In this paper we ﬁrst consider the problem of detecting the set of torus knots T.p;q/ in S3using knot invariants. To reach this goal neither knot Floer homology nor the A– polynomial alone is enough: The torus knot T.4;3/has the same knot Floer homology 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]). christmas tree michaels canadaWebWe 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 ... get password policy powershell azure ad

"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. " - Knot floer homology detect unlink

Knot floer homology detect unlink

FraserBinnsandGageMartin arXiv:2011.02005v1 …

Webits knot Floer homology, implying that Floer homology solves the word problem for mapping class groups of surfaces with non-empty boundary. Finally, we survey some conjectures and questions and, based on the results described above, formulate some new ones. The ﬁrst author was partially supported by NSF Grants DMS-0706979 DMS-0906258, CAREER 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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WebHeegaard 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. 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.

Web3 KnotFloer homology detects Jn Given that knot Floer homology detects the genus of a link, it is natural to try and detect links of small genus. The one component case is that of … 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 …

WebKhovanov 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. WebNov 3, 2024 · We give new link detection results for knot and link Floer homology inspired by recent work on Khovanov homology. We show that knot Floer homology detects $T(2,4)$, …

WebJul 6, 2006 · Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in . We will prove this conjecture for null-homologous knots in arbitrary closed 3- …

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 … christmas tree mini lightsWebWe show that link Floer homology detection results for the (2;2n) cables of the remaining knots that knot Floer homology is currently known to detect; namely the trefoils and the gure eight. Theorem 5.1. Link Floer homology detects T(2;3) 2;2nfor all n. Note here that the (2;2n)-cable of T(2;3) is the (2; 2n)-cable of T(2; 3). Theorem 5.2. get passwords for animal jamWebSep 20, 2007 · Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in S 3. We will prove this conjecture for null-homologous knots in arbitrary closed 3 … get password hash from active directoryWebIf there is a unique link with given knot Floer homology, we say knot Floer ho-mology “detects” that link. The first detection results given were for simple knots; Ozsv´ath … get password of connected wifi windows 11http://www.its.caltech.edu/~yini/Published/DetectTorus.pdf christmas tree mini lights green wireWebMar 18, 2024 · The only knot whose knot group is Z is the unknot, hence each L i is an unknot. So, yes, if π 1 ( S 3 − L) is a free group on n generators, then L is an n -component … christmas tree minimalist decorWebknot 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 ... get passwords from chrome to edge