Knot floer homology detect unlink

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August undefined, 2024

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 … 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]).

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http://www.its.caltech.edu/~yini/Published/DetectTorus.pdf 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 … list of companies in administration uk

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WebLagrangian 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 WebThe exact triangle is a key calculational tool in Heegaard Floer homology. It relates 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 ... 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 … images purple flowers

Knot Floer homology, link Floer homology and link detection

WebNov 10, 2024 · The fundamental group of the knot complement (the knot group) is isomorphic to Z if and only if the knot is unknotted. The A-polynomial (not to be confused … WebWe 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 ... images pushing stroller while textingWebits 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 list of companies in addis ababa

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Knot floer homology detect unlink

Khovanov homology is an unknot-detector SpringerLink

WebKnot 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]. 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.

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WebAN INTRODUCTION TO KNOT FLOER HOMOLOGY CIPRIAN MANOLESCU Abstract. This 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 dia-grams, and a combinatorial description in terms of the cube of resolutions. We discuss the ... 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...

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.

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- …

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.

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 … images putin\u0027s daughtersWebLink 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 … list of companies in accraWebWe 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 $T(2,4)$, $T(2,6)$, … images putin horseback ridingWebThe 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 list of companies hiring in ohioWebHeegaard 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. images pxeboot vmlinuz has invalid signatureWebIf 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 … image sql server c#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 ... images publishing alfreton