The mapping class group cannot be realized by homeomorphisms

Vladimir Markovic; Dragomir Saric

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arXiv · 0807.0182

The mapping class group cannot be realized by homeomorphisms

Vladimir Markovic·Dragomir Saric

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Abstract

Let $M$ be a closed surface. By $\Homeo(M)$ we denote the group of orientation preserving homeomorphisms of $M$ and let $\MC(M)$ denote the Mapping class group. In this paper we complete the proof of the conjecture of Thurston that says that for any closed surface $M$ of genus $\g \ge 2$, there is no homomorphic section $\E:\MC(M) \to \Homeo(M)$ of the standard projection map $\Proj:\Homeo(M) \to \MC(M)$.

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Vladimir Markovic, Dragomir Saric. 2008-07-01. The mapping class group cannot be realized by homeomorphisms. https://arxiv.org/abs/0807.0182

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