Some groups of mapping classes not realized by diffeomorphisms

Details Some groups of mapping classes not realized by diffeomorphisms Some groups of mapping classes not realized by diffeomorphisms

2009-05-14

arxiv.org/abs/0905.2360v1

Mathematics

Geometric Topology

14 pages

Scientific paper

Let S be a closed surface of genus g >= 2 and z in S a marked point. We prove that the subgroup of the mapping class group Map(S,z) corresponding to the fundamental group pi_1(S,z) of the closed surface does not lift to the group of diffeomorphisms of S fixing z. As a corollary, we show that the Atiyah-Kodaira surface bundles admit no invariant flat connection, and obtain another proof of Morita's non-lifting theorem.

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