Complex cycles on real algebraic models of a smooth manifold
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- by J. Bochnak and W. Kucharz PDF
- Proc. Amer. Math. Soc. 114 (1992), 1097-1104 Request permission
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 $X$.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 1097-1104
- MSC: Primary 57R19; Secondary 14C22, 14C25, 14P25
- DOI: https://doi.org/10.1090/S0002-9939-1992-1093594-2
- MathSciNet review: 1093594