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.
Publié le : 2001-09-14
Classification:
Links,
genus and central class coverings,
genera of homology classes,
57M25,
57M12,
11R
@article{1148393034,
author = {Morishita, Masanori},
title = {A theory of genera for cyclic coverings of links},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {77},
number = {10},
year = {2001},
pages = { 115-118},
language = {en},
url = {http://dml.mathdoc.fr/item/1148393034}
}
Morishita, Masanori. A theory of genera for cyclic coverings of links. Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, pp. 115-118. http://gdmltest.u-ga.fr/item/1148393034/