Homology classes of real algebraic sets

Kucharz, Wojciech

Annales de l'Institut Fourier, Tome 58 (2008) no. 3, pp. 989-1022.

Il existe un vaste programme de recherche portant sur la comparaison entre catégories topologiques et algébriques, dont l’origine remonte à 1952 avec les travaux célèbres de J. Nash sur les variétés algébriques réelles lisses. Ce papier est une contribution à ce programme. Il contient l’étude des classes d’homologie et de cohomologie représentées par des ensembles algébriques réels. En particulier, de telles classes sont étudiées dans les modèles algébriques de variétés lisses.

There is a large research program focused on comparison between algebraic and topological categories, whose origins go back to 1952 and the celebrated work of J. Nash on real algebraic manifolds. The present paper is a contribution to this program. It investigates the homology and cohomology classes represented by real algebraic sets. In particular, such classes are studied on algebraic models of smooth manifolds.

Classification : 14P05, 14P25, 14C25, 14F25
Keywords: Real algebraic variety, algebraic cycles, cohomology
Mot clés : Variété algébrique réelle, cycles algébriques, cohomologie

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