Some groups of mapping classes not realized by diffeomorphisms
Geometric Topology
2013-03-13 v2 Group Theory
Abstract
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.
Cite
@article{arxiv.0905.2360,
title = {Some groups of mapping classes not realized by diffeomorphisms},
author = {Mladen Bestvina and Thomas Church and Juan Souto},
journal= {arXiv preprint arXiv:0905.2360},
year = {2013}
}
Comments
15 pages. Final version, to appear in Comm. Math. Helv