Comptes Rendus
no. 17-18
Complex Analysis
Oka manifolds
[Les varietes de Oka]

Présenté par : Mikhaël Gromov

Franc Forstnerič1
1 Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1017-1020.

Nous donnons une réponse positive à la question suivante posée par Gromov [Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc. 2 (1989) 851–897, 3.4.(D), p. 881] : Si une variété analytique complexe Y est telle que toute application holomorphe d'un voisinage d'un sous-ensemble compact convexe de l'espace euclidien Cn dans Y peut être approximée par des applications entière de Cn dans Y, alors les applications holomorphes d'un espace de Stein réduit X dans Y possèdent la propriété d'Oka paramétrique.

We give a positive answer to Gromov's question [Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc. 2 (1989) 851–897, 3.4.(D), p. 881]: If every holomorphic map from a compact convex set in a Euclidean space Cn to a certain complex manifold Y is a uniform limit of entire maps Cn→Y, then Y enjoys the parametric Oka property. In particular, for any reduced Stein space X the inclusion O(X,Y)↪C(X,Y) of the space of holomorphic maps into the space of continuous maps is a weak homotopy equivalence.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.07.005

Franc Forstnerič 1

1 Faculty of Mathematics and Physics, University of Ljubljana, and Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia 
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Franc Forstnerič. Oka manifolds. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1017-1020. doi : 10.1016/j.crma.2009.07.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.07.005/

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