Geodesic
On~cohomology classes defined by the real points of a real algebraic $\operatorname{GM}$-surface
Izvestiya. Mathematics , Tome 43 (1994) no. 2, pp. 385-395.

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The cohomology classes $x_i=[X_i]^*\in H^2(X(\mathbb C),\mathbb Z)$ are studied, where $X_1,\dots,X_m$ are the connected components of the set of real points $X(\mathbb R)$ of a real algebraic $\operatorname{GM}$-surface $X$ and $X(\mathbb R)=X_1\cup\dots\cup X_m$ is assumed to be orientable. The results are applied to obtain congruences for the Euler characteristic of $X(\mathbb R)$. 
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V. A. Krasnov. On~cohomology classes defined by the real points of a real algebraic $\operatorname{GM}$-surface. Izvestiya. Mathematics , Tome 43 (1994) no. 2, pp. 385-395. http://geodesic.mathdoc.fr/item/IM2_1994_43_2_a10/

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