Signatures of links and finite type invariants of cyclic branched covers
Stavros Garoufalidis
Abstract
Recently, Mullins calculated the Casson-Walker invariant of the 2-fold cyclic branched cover of an oriented link in S3 in terms of its Jones polynomial and its signature, under the assumption that the 2-fold branched cover is a rational homology 3-sphere. Using elementary principles, we provide a similar calculation for the general case. In addition, we calculate the LMO invariant of the p-fold branched cover of twisted knots in S3 in terms of the Kontsevich integral of the knot.
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