We give a short and elementary proof of the nonrealizability of the mapping class group via homeomorphisms. This was originally established by Markovic, resolving a conjecture of Thurston. With the tools established in this paper, we also obtain some rigidity results for actions of the mapping class group on Euclidean spaces.

中文翻译：

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映射类群动作的全局不动点与马尔科维奇定理

我们通过同胚给出了映射类群的不可实现性的简短而基本的证明。这最初是由马尔科维奇建立的，解决了瑟斯顿的一个猜想。利用本文建立的工具，我们还获得了映射类群在欧几里得空间上的一些刚性结果。