{"paper":{"title":"The action of matrix groups on aspherical manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.AT","authors_text":"Shengkui Ye","submitted_at":"2016-09-25T04:17:44Z","abstract_excerpt":"Let $\\mathrm{SL}_{n}(\\mathbb{Z})$ $(n\\geq 3)$ 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 conjec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07699","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}