## 抄録

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 S^{3}. Therefore, the first non-vanishing coefficient of the Conway polynomial is determined by the linking numbers in S^{3}. This generalizes a result of Hoste.

本文言語 | English |
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ページ（範囲） | 631-640 |

ページ数 | 10 |

ジャーナル | Journal of Knot Theory and its Ramifications |

巻 | 16 |

号 | 5 |

DOI | |

出版ステータス | Published - 2007 5月 |

外部発表 | はい |

## ASJC Scopus subject areas

- 代数と数論