Steenrod squares on conjugation spaces

We prove that the coefficients of the so-called conjugation equation for conjugation spaces in the sense of Hausmann–Holm–Puppe are completely determined by Steenrod squares. This generalises a result of V.A. Krasnov for certain complex algebraic varieties. It also leads to a generalisation of a formula given by Borel and Haefliger, thereby largely answering an old question of theirs in the affirmative. To cite this article: M. Franz, V. Puppe, C. R. Acad. Sci. Paris, Ser. I 342 (2006).