paper

The mapping class group cannot be realized by homeomorphisms

arXiv:0807.0182

Abstract

Let be a closed surface. By $\Homeo(M)$ we denote the group of orientation preserving homeomorphisms of 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 of genus $\g \ge 2$, there is no homomorphic section $\E:\MC(M) \to \Homeo(M)$ of the standard projection map $\Proj:\Homeo(M) \to \MC(M)$.

33 pages, 6 figures

The mapping class group cannot be realized by homeomorphisms · wovepaper