1992
DOI: 10.1090/s0002-9939-1992-1093594-2
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Complex cycles on real algebraic models of a smooth manifold

Abstract: Abstract. Let M be a compact connected orientable C°° submanifold of R" with 2 dim M + 1 < n . Let G be a subgroup of H2(M, Z) such that the quotient group H2(M,Z) has no torsion. Then M can be approximated in R" by a nonsingular algebraic subset X such that H^.(X, Z) is isomorphic to G. Here H£_. (X,Z) denotes the subgroup of H2(X,Z) generated by the cohomology classes determined by the complex algebraic hypersurfaces in a complexification of X .

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Cited by 4 publications
(2 citation statements)
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“…We say that a topological F-vector bundle on X (R) admits an algebraic structure if it is isomorphic to E(F)| X (R) for some U and E as above. This terminology is consistent with that used in [6,10,11,13], X (R) being Zariski dense in X . In this section, we are interested in the subgroup…”
Section: Algebraic Models and Vector Bundlesmentioning
confidence: 59%
“…We say that a topological F-vector bundle on X (R) admits an algebraic structure if it is isomorphic to E(F)| X (R) for some U and E as above. This terminology is consistent with that used in [6,10,11,13], X (R) being Zariski dense in X . In this section, we are interested in the subgroup…”
Section: Algebraic Models and Vector Bundlesmentioning
confidence: 59%
“…Recall that a nonsingular real algebraic variety diffeomorphic to a ^c o manifold M is called an algebraic model of M. Every closed ^ manifold admits uncountably many pail-wise biregularly nonisomorphic algebraic models [6]. The following facts are known: (i) Every closed ^°° manifold M has an algebraic model X such that ^(X S 2 ) is dense in ^°(X, S 2 ) and VB^(X) = VB^(X) [8,Theorem 1.2].…”
Section: (X Z) ^([/]) = Hv) (K)mentioning
confidence: 99%