On signatures associated with ramified coverings and embedding problems
Wood, J. ; Thomas, Emery
Annales de l'Institut Fourier, Tome 23 (1973), p. 229-235 / Harvested from Numdam
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Étant donné une classe de cohomologie ξ∈H 2 (M;Z), il existe une sous-variété K⊂M duale à ξ dans le sens de Poincaré. Il existe un ensemble de tels plongements qui est caractérisé par des propriétés topologiques, que les hypersurfaces algébriques de CP n vérifient. Cet exposé résume quelques résultats sur la question : comment la divisibilité de ξ limite-t-elle les sous-variétés duales, K, dans cet ensemble ? Et nous donnons une formule pour la signature associée à un revêtement d’ordre d sur M, ramifiée sur K ; nous le démontrons dans le cas où d=2.

Given a cohomology class ξ∈H 2 (M;Z) there is a smooth submanifold K⊂M Poincaré dual to ξ. A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in CP n . This note summarizes some results on the question: how does the divisibility of ξ restrict the dual submanifolds K in this class ? A formula for signatures associated with a d-fold ramified cover of M branched along K is given and a proof is included in case d=2.

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     author = {Wood, J. and Thomas, Emery},
     title = {On signatures associated with ramified coverings and embedding problems},
     journal = {Annales de l'Institut Fourier},
     volume = {23},
     year = {1973},
     pages = {229-235},
     doi = {10.5802/aif.470},
     mrnumber = {49 \#3964},
     zbl = {0262.57012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1973__23_2_229_0}
}

Wood, J.; Thomas, Emery. On signatures associated with ramified coverings and embedding problems. Annales de l'Institut Fourier, Tome 23 (1973) pp. 229-235. doi : 10.5802/aif.470. http://gdmltest.u-ga.fr/item/AIF_1973__23_2_229_0/

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