Dragomir Saric

Title: The mapping class group cannot be realized by homeomorphisms

Abstract: Let $M$ be a closed surface. Let $Homeo(M)$ be the group of
orientation preserving homeomorphisms of $M$ and let $MC(M)$ be the
Mapping class group. Markovic proved the conjecture of Thurston that
 there is no homomorphic section $\E:MC(M) \to Homeo(M)$ of the
standard projection map $Proj:Homeo(M) \to MC(M)$ when the genus of
$M$ is at least six. We complete the proof of the conjecture of
Thurston for closed surfaces of genus at least two. Our methods give a
unified proof for any genus. Joint work with V. Markovic.