A combinatorial spanning tree model for knot Floer homology
نویسندگان
چکیده
منابع مشابه
A 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.
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Similar to knots in S, any knot in a lens space has a grid diagram from which one can combinatorially compute all of its knot Floer homology invariants. We give an explicit description of the generators, differentials, and rational Maslov and Alexander gradings in terms of combinatorial data on the grid diagram. Motivated by existing results for the Floer homology of knots in S and the similari...
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In this paper, we introduce a simple combinatorial method for computing all versions (∧,+,−,∞) of the knot Floer homology of the preimage of a two-bridge knot Kp,q inside its double-branched cover, −L(p, q). The 4-pointed genus 1 Heegaard diagram we obtain looks like a twisted version of the toroidal grid diagrams recently introduced by Manolescu, Ozsváth, and Sarkar. We conclude with a discuss...
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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 کاملA Spanning Tree Model for the Heegaard Floer Homology of a Branched Double-cover
Given a diagram of a link K in S, we write down a Heegaard diagram for the brancheddouble cover Σ(K). The generators of the associated Heegaard Floer chain complex correspond to Kauffman states of the link diagram. Using this model we make some computations of the homology d HF (Σ(K)) as a graded group. We also conjecture the existence of a δ-grading on d HF (Σ(K)) analogous to the δ-grading on...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2012
ISSN: 0001-8708
DOI: 10.1016/j.aim.2012.06.006