Non-realizability of subgroups of mapping class groups

Non-realizability of subgroups of mapping class groups

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Lei Chen, California Institute of Technology
Fine Hall 314

Nielsen realization problem asks whether subgroups of mapping class group can be realized as a subgroup in homeomorphism groups of the surface. This problem is closely related to whether surface bundles have topological flat structures. In this talk, I will give a proof for the whole group which essentially uses torsions. Then I will present a joint work with V. Markovic where we deal with one case when the group is torsion-free. We give a partial result that the Torelli group has no realization in area-preserving homeomorphisms.