Cohomological obstructions to Nielsen realization

Abstract

For a based manifold (M,*), the question of whether the surjection Diff(M,*) \rightarrow π_0 Diff(M,*) admits a section is an example of a Nielsen realization problem. This question is related to a question about flat connections on M-bundles and is meaningful for M of any dimension. In dimension 2, Bestvina-Church-Souto showed a section does not exist when M is closed and has genus g\ge 2. Their techniques are cohomological and certain aspects are specific to surfaces. We give new cohomological techniques to generalize their result to many locally symmetric manifolds. The main tools include Chern-Weil theory, Milnor-Wood inequalities, and Margulis superrigidity.

27 pages, final version, accepted for publication by the Journal of Topology

References in corpus (2)

• Groups acting on manifolds: around the Zimmer program
• Pinched smooth hyperbolization

Cited by in corpus (2)

• Dehn twists and the Nielsen realization problem for spin 4-manifolds
• Pontryagin classes of locally symmetric manifolds