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Type: Book chapter
Title: Applications of a parametric Oka principle for liftings
Author: Larusson, F.
Citation: Complex Analysis, 2010 / Ebenfelt, P., Hungerbuhler, N., Kohn, J., Mok, N., Straube, E. (ed./s), pp.205-211
Publisher: Springer
Publisher Place: Switzerland
Issue Date: 2010
Series/Report no.: Trends in Mathematics
ISBN: 9783034600088
Editor: Ebenfelt, P.
Hungerbuhler, N.
Kohn, J.
Mok, N.
Straube, E.
Statement of
Finnur Lárusson
Abstract: A parametric Oka principle for liftings, recently proved by Forstnerič, provides many examples of holomorphic maps that are fibrations in a model structure introduced in previous work of the author. We use this to show that the basic Oka property is equivalent to the parametric Oka property for a large class of manifolds. We introduce new versions of the basic and parametric Oka properties and show, for example, that a complex manifold X has the basic Oka property if and only if every holomorphic map to X from a contractible submanifold of Cn extends holomorphically to Cn.
Keywords: Stein manifold
Oka principle
Oka property
convex interpolation property
model structure
Rights: Copyright 2010 Springer Basel AG
DOI: 10.1007/978-3-0346-0009-5
Appears in Collections:Aurora harvest 5
Mathematical Sciences publications

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