Geodesic
On the cohomology of real algebraic varieties
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 112-151

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A class of spaces with involution introduced by the author is studied:effective spaces, whose cohomology rings of fixed-point sets are completely determined by the spectral sequence of involution. Real algebraic varieties admitting a “cellular decomposition” are effective $M$-spaces. Under certain restrictions, one calculates the spectral sequence of involution and the total $\mathbb Z_2$ Betti number of the real part for real subvarieties of real algebraic varieties that are effective $GM$-spaces. 
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     author = {I. O. Kalinin},
     title = {On the cohomology of real algebraic varieties},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a7/}
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I. O. Kalinin. On the cohomology of real algebraic varieties. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 112-151. http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a7/