Geodesic
On Bordisms of Real Algebraic $M$-Varieties
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 724-732.

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Any morphism of nonsingular complete real algebraic varieties $F\colon Y\to X$ determines a holomorphic mapping of the sets of complex points $F_{\mathbb C}\colon Y(\mathbb C)\to X(\mathbb C)$ as well as a differentiable mapping of the sets of real points $F_{\mathbb R}\colon Y(\mathbb R)\to X(\mathbb R)$. These two mappings determine classes of nonoriented bordisms $[F_{\mathbb C}]\in\operatorname{MO}_{2m}(X(\mathbb C))$, $[F_{\mathbb R}]\in\operatorname{MO}_m(X(\mathbb R))$, where $m=\dim Y$. The paper describes relationship between these two classes of bordisms.
Keywords: real holomorphic variety, real $M$-variety, nonoriented bordism, cohomology operations, Harnack–Thom inequality, Leray spectral sequence.
Mots-clés : equivariant bordism 
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V. A. Krasnov. On Bordisms of Real Algebraic $M$-Varieties. Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 724-732. http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a9/

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