Classification des formes de Seifert rationnelles des germes de courbe plane
Bois, Philippe Du ; Hunault, Ollivier
Annales de l'Institut Fourier, Tome 46 (1996), p. 371-410 / Harvested from Numdam
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Nous donnons une description explicite de la forme de Seifert rationnelle associée à un germe de courbe plane, à isomorphisme près ou à Witt-équivalences près, en termes d’un ensemble complet d’invariants déterminé à partir du type topologique du germe. Ces invariants sont liés à la classification des formes hermitiennes sur les extensions cyclotomiques de ℚ et à celle des formes quadratiques sur ℚ.

En application, nous trouvons des nœuds algébriques cobordants et non isotopes dont la monodromie est d’ordre fini.

We give an explicit description of the rational Seifert form associated with a plane curve germ, up to isomorphism or up to Witt-equivalence, in terms of a complete set of invariants determined by the topological type of the germ. The invariants are related to the classification of hermitian forms on cyclotomic extensions of ℚ and of quadratic forms on ℚ.

As an application, we find cobordant and nonisotopic algebraic knots, the monodromy of which is of finite order.

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     author = {Bois, Philippe Du and Hunault, Ollivier},
     title = {Classification des formes de Seifert rationnelles des germes de courbe plane},
     journal = {Annales de l'Institut Fourier},
     volume = {46},
     year = {1996},
     pages = {371-410},
     doi = {10.5802/aif.1518},
     mrnumber = {97g:32048},
     zbl = {0854.32021},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1996__46_2_371_0}
}

Bois, Philippe Du; Hunault, Ollivier. Classification des formes de Seifert rationnelles des germes de courbe plane. Annales de l'Institut Fourier, Tome 46 (1996) pp. 371-410. doi : 10.5802/aif.1518. http://gdmltest.u-ga.fr/item/AIF_1996__46_2_371_0/

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