Knot floer homology detect unlink

Author: ocmc

August undefined, 2024

WebMar 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 … 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- …

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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 $T(2,4)$, … gyba schedule

Khovanov module and the detection of unlinks Request PDF

http://www.its.caltech.edu/~yini/Published/DetectTorus.pdf 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 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... gybbon rise staplehurst

general topology - A knot invariant which highlights the …

Ribbon Concordance and Link Homology Theories - Duke …

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 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]). gy baptistry\u0027sWebLagrangian 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 boys name with an n

"WebFloer’s surgery long exact sequence for instanton Floer homology. It can be seen as an extension of a more straightforward property of I\.K/, namely that it has a long exact … " - Knot floer homology detect unlink

Knot floer homology detect unlink

Heegaard Floer Homology and Link Detection

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 ... 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.

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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 … 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.

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 … WebIf 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 …

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 … 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 …

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 ...

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… boys name with bWebThe 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 ... boys name with a zWebAug 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 … gyazo vs lightshot reddit