Computing knot Floer homology in cyclic branched covers
نویسندگان
چکیده
منابع مشابه
Knot Floer homology in cyclic branched covers
In this paper, we introduce a sequence of invariants of a knot K in S3 : the knot Floer homology groups ĤFK(Σm(K); K̃, i) of the preimage of K in the m–fold cyclic branched cover over K . We exhibit ĤFK(Σm(K); K̃, i) as the categorification of a well-defined multiple of the Turaev torsion of Σm(K)− K̃ in the case where Σm(K) is a rational homology sphere. In addition, when K is a two-bridge knot, ...
متن کاملComputing Knot Floer Homology in Cyclic Branched Covers
We use grid diagrams to give a combinatorial algorithm for computing the knot Floer homology of the pullback of a knot K in its m-fold cyclic branched cover Σm(K), and we give computations when m = 2 for over fifty three-bridge knots with up to eleven crossings.
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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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Let L be a link in A×I where A is an annulus. We consider A×I to be embedded in R2×R respecting the obvious fibration and embedding A into a round annulus in R2. We always project L into R2 (or A) along the R-fibration. The complement of L in A × I is thereby identified with the complement of B∪L in S3 where B an unknot as depicted below, called the axis of L. We assume throughout that L inters...
متن کاملOn the Heegaard Floer Homology of Branched Double-covers
Let L ⊂ S be a link. We study the Heegaard Floer homology of the branched double-cover Σ(L) of S, branched along L. When L is an alternating link, ĤF of its branched double-cover has a particularly simple form, determined entirely by the determinant of the link. For the general case, we derive a spectral sequence whose E term is a suitable variant of Khovanov’s homology for the link L, convergi...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2008
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2008.8.1163