### Abstract

Following the conceptual analogies between knots and primes, 3-manifolds and number fields, we discuss an analogue in knot theory after the model of the arithmetical theory of genera initiated by Gauss. We present an analog for cyclic coverings of links following along the line of Iyanaga-Tamagawa's genus theory for cyclic extentions over the rational number field. We also give examples of Z/2Z × Z/2Z-coverings of links for which the principal genus theorem does not hold.

Original language | English |
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Pages (from-to) | 115-118 |

Number of pages | 4 |

Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |

Volume | 77 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jan 1 2001 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

**A theory of genera for cyclic coverings of links.** / Morishita, Masanori.

Research output: Contribution to journal › Article

*Proceedings of the Japan Academy Series A: Mathematical Sciences*, vol. 77, no. 7, pp. 115-118. https://doi.org/10.3792/pjaa.77.115

}

TY - JOUR

T1 - A theory of genera for cyclic coverings of links

AU - Morishita, Masanori

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Following the conceptual analogies between knots and primes, 3-manifolds and number fields, we discuss an analogue in knot theory after the model of the arithmetical theory of genera initiated by Gauss. We present an analog for cyclic coverings of links following along the line of Iyanaga-Tamagawa's genus theory for cyclic extentions over the rational number field. We also give examples of Z/2Z × Z/2Z-coverings of links for which the principal genus theorem does not hold.

AB - Following the conceptual analogies between knots and primes, 3-manifolds and number fields, we discuss an analogue in knot theory after the model of the arithmetical theory of genera initiated by Gauss. We present an analog for cyclic coverings of links following along the line of Iyanaga-Tamagawa's genus theory for cyclic extentions over the rational number field. We also give examples of Z/2Z × Z/2Z-coverings of links for which the principal genus theorem does not hold.

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UR - http://www.scopus.com/inward/citedby.url?scp=23044528973&partnerID=8YFLogxK

U2 - 10.3792/pjaa.77.115

DO - 10.3792/pjaa.77.115

M3 - Article

AN - SCOPUS:23044528973

VL - 77

SP - 115

EP - 118

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

SN - 0386-2194

IS - 7

ER -