Geodesic
Real algebraic varieties and cobordism
Izvestiya. Mathematics , Tome 71 (2007) no. 3, pp. 573-601.

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We consider two non-oriented cobordism classes that are obtained from a projective morphism of smooth real quasi-projective algebraic varieties. The first is induced by the map of complex points of the varieties and the second by the map of real points. We find and prove relations between these cobordism classes. In particular, we describe the restrictions imposed on the first by the vanishing of the second. 
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V. A. Krasnov. Real algebraic varieties and cobordism. Izvestiya. Mathematics , Tome 71 (2007) no. 3, pp. 573-601. http://geodesic.mathdoc.fr/item/IM2_2007_71_3_a6/

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