On homology of real algebraic varieties

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Ozan Y.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.129, no.11, pp.3167-3175, 2001 (SCI-Expanded) identifier identifier


Let R be a commutative ring with unity and X an R-oriented compact nonsingular real algebraic variety of dimension n. If i : X --> X-C is any nonsingular complexification of X, then the kernel, which we will denote by KHk(X, R), of the induced homomorphism i(*) : H-k(X, R) --> H-k(X-C, R) is independent of the complexification. In this work, we study KHk(X, R) and give some of its applications.