On homology of real algebraic varieties

Ozan, Yıldıray

doi:10.1090/S0002-9939-01-06065-8

On homology of real algebraic varieties
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Proc. Amer. Math. Soc. 129 (2001), 3167-3175 Request permission

Abstract:

Let $R$ be a commutative ring with unity and $X$ an $R$-oriented compact nonsingular real algebraic variety of dimension $n$. If $i :X \rightarrow X_{\mathbb C}$ is any nonsingular complexification of $X$, then the kernel, which we will denote by $KH_k(X, R)$, of the induced homomorphism ${i}_*:H_k(X,R) \rightarrow H_k(X_{\mathbb C},R)$ is independent of the complexification. In this work, we study $KH_k(X, R)$ and give some of its applications.

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