Abstract
Let for be the special linear group and be a closed aspherical manifold. It is proved that when , a group action of on by homeomorphisms is trivial if and only if the induced group homomorphism is trivial. For (almost) flat manifolds, we prove a similar result in terms of holonomy groups. In particular, when is nilpotent, the group cannot act nontrivially on when . This confirms a conjecture related to Zimmer’s program for these manifolds.
Citation
Shengkui Ye. "The action of matrix groups on aspherical manifolds." Algebr. Geom. Topol. 18 (5) 2875 - 2895, 2018. https://doi.org/10.2140/agt.2018.18.2875
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