Geodesic
On~homology classes determined by real points of a real algebraic variety
Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 277-297.

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For a nonsingular $n$-dimensional real projective algebraic variety $X$ the set $X(\mathbf R)$ of its real points is the union of connected components $X(\mathbf R)=X_1\cup\dots\cup X_m$. Those components give rise to homology classes $[X_1],\dots,[X_m]\in H_n(X(\mathbf C),\mathbf F_2)$. In this paper a bound on the number of relations between those homology classes is obtained. 
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V. A. Krasnov. On~homology classes determined by real points of a real algebraic variety. Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 277-297. http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a2/

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