A theory of genera for cyclic coverings of links

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6 Citations (Scopus)

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 languageEnglish
Pages (from-to)115-118
Number of pages4
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume77
Issue number7
DOIs
Publication statusPublished - 2001

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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