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- Title
Cohomological obstructions to Nielsen realization.
- Authors
Tshishiku, Bena
- Abstract
For a based manifold (M,*), the question of whether the surjective homomorphism Diff(M,*)→π0Diff(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 ['Some groups of mapping classes not realized by diffeomorphisms', Comment. Math. Helv. 88 (2013) 205-220] showed a section does not exist when M is closed and has genus g≥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.
- Subjects
COHOMOLOGY theory; OBSTRUCTION theory; NIELSEN'S form; HOMOMORPHISMS; DIFFEOMORPHISMS; MATHEMATICAL inequalities
- Publication
Journal of Topology, 2015, Vol 8, Issue 3, p352
- ISSN
1753-8416
- Publication type
Article
- DOI
10.1112/jtopol/jtu028