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J. Wood; Emery Thomas
On signatures associated with ramified coverings and embedding problems
Annales de l'institut Fourier, 23 no. 2 (1973), p. 229-235, doi: 10.5802/aif.470
Article PDF | Reviews MR 49 #3964 | Zbl 0262.57012

Résumé - Abstract

Given a cohomology class $\xi \in H^2(M;Z)$ there is a smooth submanifold $K\subset M$ Poincaré dual to $\xi $. A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in ${\bf C}P_n$. This note summarizes some results on the question: how does the divisibility of $\xi $ 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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