Dragomir Saric, Queens College, CUNY

TITLE: The mapping class group cannot be realized by homeomorphisms

ABSTRACT: Let $S$ be a closed surface of genus at least two.  The mapping class group $MC(S)$ is the quotient of the group of homeomorphisms $Homeo(S)$ by the normal subgroup of homeomorphisms
$Homeo_0(S)$ which are homotopic to the identity. The natural projection $Pr:Homeo(S)\to MC(S)=Homeo(S)/Homeo_0(S)$ is a group homomorphism. Nielsen asked whether there exists a homomorphic section $E:MC(S)\to Homeo(S)$. Namely, the question is whether $MC(S)$ can be realized as a subgroup of $Homeo(S)$. We show that this is not possible for all surfaces of genus at least two.  This is joint work with V. Markovic.