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The mapping class group cannot be realized by homeomorphisms

#### Dragomir Saric, CUNY Queens

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.