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On signatures associated with ramified coverings and embedding problems

J. WoodEmery Thomas — 1973

Annales de l'institut Fourier

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 C P 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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