映射柱与Oka原理
Mapping Cylinders and the Oka Principle
摘要：
我们应用概念和工具，从抽象同伦理论到复分析和几何，继续我们的发展的想法，奥卡原则是关于在适当的模型结构的不相容性。我们明确因素的全纯映射之间的Stein流形通过映射柱在三个不同的模型结构，并使用这些分解证明表面上不同的Oka性质的复流形和全纯映射之间的影响。我们表明，对于Stein流形，几个Oka性质相吻合，其特征在于椭圆的几何条件。超越Stein情形，研究任意复流形的凝聚模型，利用Jouanolou技巧，我们得到了一大类流形的Oka性质的几何刻画，推广了Stein流形的结果.最后，我们证明了一个逆奥卡原则说，某些概念的凝聚流形是等价的斯坦。
英文摘要：
We apply concepts and tools from abstract homotopy theory to complex analysis and geometry, continuing our development of the idea that the Oka Principle is about fibrancy in suitable model structures. We explicitly factor a holomorphic map between Stein manifolds through mapping cylinders in three different model structures and use these factorizations to prove implications between ostensibly different Oka properties of complex manifolds and holomorphic maps. We show that for Stein manifolds, several Oka properties coincide and are characterized by the geometric condition of ellipticity. Going beyond the Stein case to a study of cofibrant models of arbitrary complex manifolds, using the Jouanolou Trick, we obtain a geometric characterization of an Oka property for a large class of manifolds, extending our result for Stein manifolds. Finally, we prove a converse Oka Principle saying that certain notions of cofibrancy for manifolds are equivalent to being Stein.
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