We show that the homotopy type of a complex manifold $X$ satisfying the Oka property is captured by holomorphic maps from the affine spaces $C^n$, $ngeq 0$, 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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机译：我们证明，满足Oka属性的复杂流形$ X $的同伦类型被全同映射从仿射空间$ C ^ n $，$ n geq 0 $捕获到$ X $中。在这样的$ X $中，所有复杂的Lie群及其同质空间。我们对这一结果进行了概括，其中之一表明，从任何光滑流形到$ X $的连续映射空间的同伦类型是由一个简单集合给出的，该简单集合的简单性是进入到$ X $的全纯映射。
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