منابع مشابه
Linking 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 کاملBranched Cyclic Covers and Finite Type Invariants
This work identifies a class of moves on knots which translate to m-equivalences of the associated p-fold branched cyclic covers, for a fixed m and any p (with respect to the Goussarov-Habiro filtration). These moves are applied to give a flexible (if specialised) construction of knots for which the Casson-Walker-Lescop invariant (for example) of their p-fold branched cyclic covers may be readi...
متن کاملFinite Type Invariants of Cyclic Branched Covers
Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parametrized by the positive integers), namely the cyclic branched coverings of the knot. In this paper we give a formula for the the Casson-Walker invariants of these 3-manifolds in terms of residues of a rational function (which measures the 2-loop part of the Kontsevich integral of a knot) and the s...
متن کاملKnot 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 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 ...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2017
ISSN: 0026-2285
DOI: 10.1307/mmj/1508810819