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 $X(\mathbb R)$. 
@article{IM2_1994_43_2_a10,
     author = {V. A. Krasnov},
     title = {On~cohomology classes defined by the real points of a real algebraic $\operatorname{GM}$-surface},
     journal = {Izvestiya. Mathematics },
     pages = {385--395},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1994_43_2_a10/}
}
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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/