A theory of genera for cyclic coverings of links

Research output: Contribution to journalArticle

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 - Jan 1 2001

Fingerprint

Genus
Covering
Number field
Analogue
Knot Theory
Knot
Gauss
Analogy
Line
Theorem
Model

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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

In: Proceedings of the Japan Academy Series A: Mathematical Sciences, Vol. 77, No. 7, 01.01.2001, p. 115-118.

Research output: Contribution to journalArticle

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