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Sept. 2001 A theory of genera for cyclic coverings of links
Masanori Morishita
Proc. Japan Acad. Ser. A Math. Sci. 77(7): 115-118 (Sept. 2001). DOI: 10.3792/pjaa.77.115


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 $\mathbf{Z} / 2\mathbf{Z} \times \mathbf{Z} / 2\mathbf{Z}$-coverings of links for which the principal genus theorem does not hold.


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Masanori Morishita. "A theory of genera for cyclic coverings of links." Proc. Japan Acad. Ser. A Math. Sci. 77 (7) 115 - 118, Sept. 2001.


Published: Sept. 2001
First available in Project Euclid: 23 May 2006

zbMATH: 1004.57001
MathSciNet: MR1857286
Digital Object Identifier: 10.3792/pjaa.77.115

Primary: 57M12 , 57M25
Secondary: 11R

Keywords: genera of homology classes , genus and central class coverings , links

Rights: Copyright © 2001 The Japan Academy


Vol.77 • No. 7 • Sept. 2001
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