Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 18, Number 5 (2018), 2875-2895.
The action of matrix groups on aspherical manifolds
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.
Algebr. Geom. Topol., Volume 18, Number 5 (2018), 2875-2895.
Received: 20 June 2017
Revised: 19 April 2018
Accepted: 3 June 2018
First available in Project Euclid: 30 August 2018
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Ye, Shengkui. The action of matrix groups on aspherical manifolds. Algebr. Geom. Topol. 18 (2018), no. 5, 2875--2895. doi:10.2140/agt.2018.18.2875. https://projecteuclid.org/euclid.agt/1535594425