### 抜粋

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 in Q(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, t ^{-1}] linking number in the infinite cyclic cover of the complement of a knot is determined by the Seifert matrix of the knot. We eliminate 'modulo Z' and 'modulo Z[t, t ^{-1}]'. When the finite cyclic cover of the 3-sphere branched over a knot is a rational homology 3-sphere, the linking number of a pair in the preimage of a link in the 3-sphere is determined by the Goeritz/Seifert matrix of the knot.

元の言語 | English |
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ページ（範囲） | 3669-3685 |

ページ数 | 17 |

ジャーナル | Transactions of the American Mathematical Society |

巻 | 356 |

発行部数 | 9 |

DOI | |

出版物ステータス | Published - 2004 9 1 |

外部発表 | Yes |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics