Oka manifolds: From Oka to Stein and back
Annales de la faculté des sciences de Toulouse Mathématiques (2013)
- Volume: 22, Issue: 4, page 747-809
- ISSN: 0240-2963
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topForstnerič, Franc. "Oka manifolds: From Oka to Stein and back." Annales de la faculté des sciences de Toulouse Mathématiques 22.4 (2013): 747-809. <http://eudml.org/doc/275300>.
@article{Forstnerič2013,
abstract = {Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations of Oka manifolds, the functorial properties of this class, and geometric sufficient conditions for being Oka, the most important of which is Gromov’s ellipticity. We survey the current status of the theory in terms of known examples of Oka manifolds, mention open problems and outline the proofs of the main results. In the appendix by F. Lárusson it is explained how Oka manifolds and Oka maps, along with Stein manifolds, fit into an abstract homotopy-theoretic framework.The article is an expanded version of lectures given by the author at Winter School KAWA 4 in Toulouse, France, in January 2013. A comprehensive exposition of Oka theory is available in the monograph [32].},
author = {Forstnerič, Franc},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Oka-Grauert principle; Stein manifolds; Oka manifolds; Gromov's ellipticity},
language = {eng},
month = {6},
number = {4},
pages = {747-809},
publisher = {Université Paul Sabatier, Toulouse},
title = {Oka manifolds: From Oka to Stein and back},
url = {http://eudml.org/doc/275300},
volume = {22},
year = {2013},
}
TY - JOUR
AU - Forstnerič, Franc
TI - Oka manifolds: From Oka to Stein and back
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2013/6//
PB - Université Paul Sabatier, Toulouse
VL - 22
IS - 4
SP - 747
EP - 809
AB - Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations of Oka manifolds, the functorial properties of this class, and geometric sufficient conditions for being Oka, the most important of which is Gromov’s ellipticity. We survey the current status of the theory in terms of known examples of Oka manifolds, mention open problems and outline the proofs of the main results. In the appendix by F. Lárusson it is explained how Oka manifolds and Oka maps, along with Stein manifolds, fit into an abstract homotopy-theoretic framework.The article is an expanded version of lectures given by the author at Winter School KAWA 4 in Toulouse, France, in January 2013. A comprehensive exposition of Oka theory is available in the monograph [32].
LA - eng
KW - Oka-Grauert principle; Stein manifolds; Oka manifolds; Gromov's ellipticity
UR - http://eudml.org/doc/275300
ER -
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