Oka manifolds and the Oka principle in complex geometry

Dr T. Ritter (University of Adelaide )

Monday 4th February, 2013 16:00-17:00 Maths 203


The class of Stein manifolds is of fundamental importance in complex geometry, consisting of those complex manifolds with a rich supply of holomorphic (that is, complex differentiable) functions into the complex numbers. Given the rigidity of holomorphic maps (in contrast to continuous maps), it is surprising that many problems involving holomorphic maps on Stein manifolds only have topological obstructions to their solution. This phenomenon is known as the 'Oka principle', and suitable target spaces for such maps are called Oka manifolds, a class recently introduced by Forstneric, building on earlier work of Gromov. I will give an introduction to Stein and Oka manifolds, and explain some of the Oka properties that maps between such manifolds satisfy. I will also say a few words about how this theory can be understood using model categories, in the holomorphic homotopy theory of Larusson.

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