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 ...
متن کاملKnot Floer Homology of (1, 1)-knots
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.
متن کاملA Combinatorial Description of Knot Floer Homology
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.
متن کاملAn Introduction to Knot Floer Homology
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...
متن کاملKnot Floer Homology and Integer Surgeries
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