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A theory of genera for cyclic coverings of links Morishita, Masanori 16189 40242515 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. journal article 日本学士院 = Japan Academy 2001-01-01 VoR application/pdf Proceedings of the Japan Academy Series A: Mathematical Sciences 7 77 115 118 AA00785474 0386-2194 https://kanazawa-u.repo.nii.ac.jp/record/10622/files/SC-PR-MORISHITA-M-115.pdf http://hdl.handle.net/2297/37864 https://kanazawa-u.repo.nii.ac.jp/records/10622 eng https://doi.org/10.3792/pjaa.77.115 http://www.japan-acad.go.jp/ http://projecteuclid.org/ Copyright © The Japan Academy