Knot Floer homology of Whitehead doubles
نویسندگان
چکیده
منابع مشابه
Floer Homology and Knot Complements
We use the Ozsváth-Szabó theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call ĈF r. It carries information about the Ozsváth-Szabó Floer homology of large integral surgeries on the knot. Using the exact triangle, we derive information about other surgeries on knots, and about the maps on ...
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We present a combinatorial method for a calculation of knot Floer homology with Z-coefficient of (1, 1)-knots, and then demonstrate it for non-alternating (1, 1)-knots with ten crossings and the pretzel knots of type (−2, m, n). Our calculations determine the unknotting numbers and 4-genera of the pretzel knots of this type.
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Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of K.
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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 diagrams, and a combinatorial description in terms of the cube of resolutions. We discuss the geometric information carried by knot Floer homology, and the connection to threeand four-dimensional topology via surge...
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Let Y be a closed three-manifold with trivial first homology, and let K ⊂ Y be a knot. We give a description of the Heegaard Floer homology of integer surgeries on Y along K in terms of the filtered homotopy type of the knot invariant for K. As an illustration of these techniques, we calculate the Heegaard Floer homology groups of non-trivial circle bundles over Riemann surfaces (with coefficie...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2007
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2007.11.2277