{"paper":{"title":"On de Rham and Dolbeault Cohomology of Solvmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Anna Fino, Hisashi Kasuya, Sergio Console","submitted_at":"2013-01-25T13:50:03Z","abstract_excerpt":"For a simply connected (non-nilpotent) solvable Lie group $G$ with a lattice $\\Gamma$ the de Rham and Dolbeault cohomologies of the solvmanifold $G/\\Gamma$ are not in general isomorphic to the cohomologies of the Lie algebra $\\mathfrak g$ of $G$. In this paper we construct, up to a finite group, a new Lie algebra $\\tilde{\\mathfrak g}$ whose cohomology is isomorphic to the de Rham cohomology of $G/\\Gamma$ by using a modification of $G$ associated with a algebraic sub-torus of the Zariski-closure of the image of the adjoint representation. This technique includes the construction due to Guan and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6042","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"}