
Table of contents for this issue  Previous article J. Wood; Emery ThomasOn signatures associated with ramified coverings and embedding problemsAnnales de l'institut Fourier, 23 no. 2 ( 1973), p. 229235, doi: 10.5802/aif.470
Article PDF  Reviews MR 49 #3964  Zbl 0262.57012
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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