Mathematics – Complex Variables
Scientific paper
2003-03-27
Mathematics
Complex Variables
Version 3 is a revision with stronger results than the earlier versions. Version 4 contains a few minor improvements
Scientific paper
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.
No associations
LandOfFree
Model Structures and the Oka Principle does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Model Structures and the Oka Principle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Model Structures and the Oka Principle will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-133023