COMPLEX CYCLES ON REAL ALGEBRAIC MODELS OF A SMOOTH MANIFOLD

Let M be a compact connected orientable C infinity submanifold of R(n) with 2 dim M + 1 less-than-or-equal-to n. Let G be a subgroup of H-2( M, Z) such that the quotient group H-2(M, Z) has no torsion. Then M ca n be approximated in R(n) by a nonsingular algebraic subset X such tha t H-2C-alg(X, Z) is isomorphic to G. Here H-2C-alg(X, Z) denotes the s ubgroup of H-2(X, Z) generated by the cohomology classes determined by the complex algebraic hypersurfaces in a complexification of X.