The mapping class group cannot be realized by homeomorphisms

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