Geodesic
The action of matrix groups on aspherical manifolds
Ye, Shengkui1
1 Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Jiangsu, China
Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2875-2895

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Let SLn(ℤ) for n ≥ 3 be the special linear group and Mr be a closed aspherical manifold. It is proved that when r < n, a group action of SLn(ℤ) on Mr by homeomorphisms is trivial if and only if the induced group homomorphism SLn(ℤ) → Out(π1(M)) is trivial. For (almost) flat manifolds, we prove a similar result in terms of holonomy groups. In particular, when π1(M) is nilpotent, the group SLn(ℤ) cannot act nontrivially on M when r < n. This confirms a conjecture related to Zimmer’s program for these manifolds.

DOI : 10.2140/agt.2018.18.2875
Classification : 57S25, 57S20, 57S17
Keywords: Nil-manifolds, aspherical manifolds, Zimmer's program, matrix group actions

Ye, Shengkui 1

1 Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Jiangsu, China 
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Ye, Shengkui. The action of matrix groups on aspherical manifolds. Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2875-2895. doi: 10.2140/agt.2018.18.2875

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