منابع مشابه
Sutured Heegaard diagrams for knots
We define sutured Heegaard diagrams for null-homologous knots in 3–manifolds. These diagrams are useful for computing the knot Floer homology at the top filtration level. As an application, we give a formula for the knot Floer homology of a Murasugi sum. Our result echoes Gabai’s earlier works. We also show that for socalled “semifibred" satellite knots, the top filtration term of the knot Floe...
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Using the combinatorial description for knot Heegaard–Floer homology, we give a generalization to singular knots that does fit in the general program of categorification of Vassiliev finite–type invariants theory. Introduction Since the categorification of the Jones polynomial by Mikhail Khovanov in 1999 [Kh00], the study of knots and links via homological invariants has remained constantly on ...
متن کاملHeegaard diagrams and Floer homology
We review the construction of Heegaard–Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link complement, the slice genus of a knot, and the unknotting number of a knot. We emphasize the application to the Thurston norm, and illustrate the theory in the ...
متن کاملChebyshev diagrams for rational knots
We show that every rational knot K of crossing number N admits a polynomial parametrization x = Ta(t), y = Tb(t), z = C(t) where Tk(t) are the Chebyshev polynomials, a = 3 and b + degC = 3N. We show that every rational knot also admits a polynomial parametrization with a = 4. If C(t) = Tc(t) is a Chebyshev polynomial, we call such a knot a harmonic knot. We give the classification of harmonic k...
متن کاملHeegaard Floer Homology and Alternating Knots
In [23] we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y , which is closely related to the Heegaard Floer homology of Y (c.f. [21]). In this paper we investigate some properties of these knot homology groups for knots in the three-sphere. We give a combinatorial description for the generators of the chain complex and their gradings. With the help of th...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2006
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2006.6.513