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arXiv 0905.05322009-05math.CVmath.AT

Oka流形中的仿射单形

Affine simplices in Oka manifolds

Finnur Larusson

备注：: A few improvements in version 2. A few more in version 3

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摘要：

本文证明了满足Oka性质的复流形X的同伦型可由仿射空间C^n，n \geq 0到X的全纯映射捕获.在这样的X中是所有复李群和它们的齐性空间。我们给出了这个结果的推广，其中之一是从任何光滑流形到X的连续映射空间的同伦型由一个单形集给出，该单形集的单形是到X的全纯映射。

英文摘要：

In this note, we show that the homotopy type of a complex manifold X satisfying the Oka property is captured by holomorphic maps from the affine spaces C^n, n\geq 0, into X. Among such X are all complex Lie groups and their homogeneous spaces. We present generalisations of this result, one of which states that the homotopy type of the space of continuous maps from any smooth manifold to X is given by a simplicial set whose simplices are holomorphic maps into X.

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