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- W3105326425 abstract "Let $mathrm{SL}_{n}(mathbb{Z})$ $(ngeq 3)$ be the special linear group and $M^{r}$ be a closed aspherical manifold. It is proved that when $r<n,$ a group action of $mathrm{SL}_{n}(mathbb{Z})$ on $M^{r}$ by homeomorphisms is trivial if and only if the induced group homomorphism $mathrm{SL}_{n}(% mathbb{Z})rightarrow mathrm{Out}(pi _{1}(M))$ is trivial. For (almost) flat manifolds, we prove a similar result in terms of holonomy groups. Especially, when $pi _{1}(M)$ is nilpotent, the group $mathrm{SL}_{n}(% mathbb{Z})$ cannot act nontrivially on $M$ when $r<n.$ This confirms a conjecture related to Zimmer's program for these manifolds." @default.
- W3105326425 created "2020-11-23" @default.
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- W3105326425 date "2018-08-22" @default.
- W3105326425 modified "2023-09-24" @default.
- W3105326425 title "The action of matrix groups on aspherical manifolds" @default.
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- W3105326425 doi "https://doi.org/10.2140/agt.2018.18.2875" @default.
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