Model Structures and the Oka Principle

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We embed the category of complex manifolds into the simplicial category of prestacks on the simplicial site of Stein manifolds, a prestack being a contravariant simplicial functor from the site to the category of simplicial sets. The category of prestacks carries model structures, one of them defined for the first time here, which allow us to develop "holomorphic homotopy theory". More specifically, we use homotopical algebra to study lifting and extension properties of holomorphic maps, such as those given by the Oka Principle. We prove that holomorphic maps satisfy certain versions of the Oka Principle if and only if they are fibrations in suitable model structures. We are naturally led to a simplicial, rather than a topological, approach, which is a novelty in analysis.
Version 3 is a revision with stronger results than the earlier versions. Version 4 contains a few minor improvements

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Complex Variables, Algebraic Topology, 32Q28 (primary); 18F10, 18F20, 18G30, 18G55, 32E10, 55U35 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/66925

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0303355
 http://arxiv.org/abs/math/0303355

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arXiv