no. 2
On signatures associated with ramified coverings and embedding problems
Annales de l'Institut Fourier, Volume 23 (1973) no. 2, pp. 229-235.

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.

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.

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Wood, J.; Thomas, Emery. On signatures associated with ramified coverings and embedding problems. Annales de l'Institut Fourier, Volume 23 (1973) no. 2, pp. 229-235. doi : 10.5802/aif.470. https://aif.centre-mersenne.org/articles/10.5802/aif.470/

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