{"paper":{"title":"Deformations and rigidity of lattices in solvable Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DG","authors_text":"Benjamin Klopsch, Oliver Baues","submitted_at":"2011-11-23T19:20:46Z","abstract_excerpt":"Let $G$ be a simply connected, solvable Lie group and $\\Gamma$ a lattice in $G$. The deformation space $\\mathcal{D}(\\Gamma,G)$ is the orbit space associated to the action of $\\Aut(G)$ on the space $\\mathcal{X}(\\Gamma,G)$ of all lattice embeddings of $\\Gamma$ into $G$. Our main result generalises the classical rigidity theorems of Mal'tsev and Sait\\^o for lattices in nilpotent Lie groups and in solvable Lie groups of real type. We prove that the deformation space of every Zariski-dense lattice $\\Gamma$ in $G$ is finite and Hausdorff, provided that the maximal nilpotent normal subgroup of $G$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5589","kind":"arxiv","version":1},"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"}