Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/68562
Type: | Journal article |
Title: | Survey of Oka theory |
Author: | Forstneric, F. Larusson, F. |
Citation: | The New York Journal of Mathematics, 2011; 17a:11-38 |
Publisher: | Electronic Journals Project |
Issue Date: | 2011 |
ISSN: | 1076-9803 1076-9803 |
Statement of Responsibility: | Franc Forstnerič and Finnur Lárusson |
Abstract: | Oka theory has its roots in the classical Oka principle in complex analysis. 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. Following a brief review of Stein manifolds, we discuss the recently introduced category of Oka manifolds and Oka maps. We consider geometric sufficient conditions for being Oka, the most important of which is ellipticity, introduced by Gromov. We explain how Oka manifolds and maps naturally fit into an abstract homotopy-theoretic framework. We describe recent applications and some key open problems. This article is a much expanded version of the lecture given by the first-named author at the conference RAFROT 2010 in Rincón, Puerto Rico, on 22 March 2010, and of a recent survey article by the second-named author, 2010. |
Keywords: | Oka principle Stein manifold elliptic manifold Oka manifold Oka map subelliptic submersion model category |
Published version: | http://nyjm.albany.edu/j/2011/17a-2.html |
Appears in Collections: | Aurora harvest Mathematical Sciences publications |
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.