A factorization of the conway polynomial and covering linkage invariants

Tatsuya Tsukamoto*, Akira Yasuhara


研究成果: Article査読

2 被引用数 (Scopus)


Levine showed that the Conway polynomial of a link is a product of two factors: one is the Conway polynomial of a knot which is obtained from the link by banding together the components; and the other is determined by the μ̄-invariants of a string link with the link as its closure. We give another description of the latter factor: the determinant of a matrix whose entries are linking pairings in the infinite cyclic covering space of the knot complement, which take values in the quotient field of ℤ[t, t -1]. In addition, we give a relation between the Taylor expansion of a linking pairing around t = 1 and derivation on links which is invented by Cochran. In fact, the coefficients of the powers of t - 1 will be the linking numbers of certain derived links in S3. Therefore, the first non-vanishing coefficient of the Conway polynomial is determined by the linking numbers in S3. This generalizes a result of Hoste.

ジャーナルJournal of Knot Theory and its Ramifications
出版ステータスPublished - 2007 5月

ASJC Scopus subject areas

  • 代数と数論


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