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 کاملLinking Numbers in Rational Homology 3-spheres, Cyclic Branched Covers and Infinite Cyclic Covers
We study the linking numbers in a rational homology 3-sphere and in the infinite cyclic cover of the complement of a knot. They take values in Q and inQ(Z[t, t−1]) respectively, where Q(Z[t, t−1]) denotes the quotient field of Z[t, t−1]. It is known that the modulo-Z linking number in the rational homology 3-sphere is determined by the linking matrix of the framed link and that the modulo-Z[t, ...
متن کاملThe homology of cyclic branched covers of S 3
Given a knot K in S 3 and a positive integer p, there is a unique p-fold cyclic connected cover X v --, S 3 K, and this can be completed to a branched cover M e --* S 3. When p is prime, the homology group H1 (M e) is torsion and was one of the earliest knot invariants (predating the Alexander polynomial). It was used by Alexander and Briggs [A-B] to distinguish knots up to 8 crossings and all ...
متن کاملCombinatorial Description of Knot Floer Homology of Cyclic Branched Covers
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...
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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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2009
ISSN: 0025-5645
DOI: 10.2969/jmsj/06120393