Some groups of mapping classes not realized by diffeomorphisms

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.

15 pages. Final version, to appear in Comm. Math. Helv

References in corpus (1)

• Global fixed points for centralizers and Morita's Theorem

Cited by in corpus (4)

• On the non-realizability of braid groups by diffeomorphisms
• On the non-realizability of braid groups by homeomorphisms
• Flat structures on surface bundles
• Cohomological obstructions to Nielsen realization