{"paper":{"title":"De Rham $2$-cohomology of real flag manifolds","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Luiz A. B. San Martin, Viviana del Barco","submitted_at":"2018-11-19T18:17:11Z","abstract_excerpt":"Let $\\mathbb{F}_{\\Theta }=G/P_{\\Theta }$ be a flag manifold associated to a non-compact real simple Lie group $G$ and the parabolic subgroup $% P_{\\Theta }$. This is a closed subgroup of $G$ determined by a subset $% \\Theta $ of simple restricted roots of $\\mathfrak{g}=Lie(G)$. This paper computes the second de Rham cohomology group of $\\mathbb{F}_\\Theta$. We prove that it zero in general, with some rare exceptions. When it is non-zero, we give a basis of $H^2(\\mathbb{F}_\\Theta,\\mathbb{R})$ through the Weil construction of closed 2-forms as characteristic classes of principal fiber bundles. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07854","kind":"arxiv","version":3},"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"}