{"paper":{"title":"Rigidity of lattices and syndetic hulls in solvable Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Oliver Ungermann","submitted_at":"2013-11-28T21:09:41Z","abstract_excerpt":"First let $G$ be a completely solvable Lie group. We recall the proof of the following result: Any closed subgroup of $G$ possesses a unique syndetic hull in $G$. As a consequence we conclude that any uniform subgroup $\\Gamma$ of $G$ is strongly rigid in the sense of G. D. Mostow: If $\\alpha:\\Gamma\\to G$ is a homomorphism of Lie groups such that $\\alpha(\\Gamma)$ is uniform in $G$, then there is an automorphism $\\varphi$ of $G$ such that $\\varphi\\,|\\,\\Gamma=\\alpha$. Now let $G$ be an arbitrary (exponential) solvable Lie group. We discuss certain conditions on closed subgroups of $G$ which are s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7426","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"}