Let be a closed surface of genus and a marked point. We prove that the subgroup of the mapping class group corresponding to the fundamental group of the closed surface does not lift to the group of diffeomorphisms of fixing . 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 this article
Mladen Bestvina, Thomas Church, Juan Souto, Some groups of mapping classes not realized by diffeomorphisms. Comment. Math. Helv. 88 (2013), no. 1, pp. 205–220DOI 10.4171/CMH/283