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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Complex cycles on real algebraic models of a smooth manifold


Authors: J. Bochnak and W. Kucharz
Journal: Proc. Amer. Math. Soc. 114 (1992), 1097-1104
MSC: Primary 57R19; Secondary 14C22, 14C25, 14P25
MathSciNet review: 1093594
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Abstract: Let $ M$ be a compact connected orientable $ {C^\infty }$ submanifold of $ {\mathbb{R}^n}$ with $ 2\dim M + 1 \leq n$. Let $ G$ be a subgroup of $ {H^2}(M,\mathbb{Z})$ such that the quotient group $ {H^2}(M,\mathbb{Z})$ has no torsion. Then $ M$ can be approximated in $ {\mathbb{R}^n}$ by a nonsingular algebraic subset $ X$ such that $ H_{\mathbb{C} \operatorname{- alg}}^{2}(X,\mathbb{Z})$ is isomorphic to $ G$. Here $ H_{\mathbb{C}\operatorname{ - alg}}^2(X,\mathbb{Z})$ denotes the subgroup of $ {H^2}(X,\mathbb{Z})$ generated by the cohomology classes determined by the complex algebraic hypersurfaces in a complexification of $ X$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1093594-2
PII: S 0002-9939(1992)1093594-2
Article copyright: © Copyright 1992 American Mathematical Society