{"paper":{"title":"Triangular de Rham Cohomology of Compact Kahler Manifolds","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DG","authors_text":"A. Brudnyi, A. Onishchik","submitted_at":"2000-01-14T20:37:58Z","abstract_excerpt":"We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principle bundle $M\\times G$ by the so-called gauge equivalence. We consider the case when M is a compact K\\\"ahler manifold and G is a solvable complex linear algebraic group of a special class which contains the Borel subgroups of all complex classical groups and, in particular, the group $T_n(\\Bbb C)$ of all triangular matrices. In this case, we get a description of the set H^1_{DR}(M,G) in terms of the 1-cohomo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001086","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"}