Affine simplices in Oka manifolds

Details Affine simplices in Oka manifolds Affine simplices in Oka manifolds

2009-05-05

arxiv.org/abs/0905.0532v3

Mathematics

Complex Variables

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

Scientific paper

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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