{"paper":{"title":"The BIC of a singular foliation defined by an abelian group of isometries","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"M. Saralegi-Aranguren, R. Wolak","submitted_at":"2004-01-28T23:57:54Z","abstract_excerpt":"We study the cohomology properties of the singular foliation $\\F$ determined by an action $\\Phi \\colon G \\times M\\to M$ where the abelian Lie group $G$ preserves a riemannian metric on the compact manifold $M$. More precisely, we prove that the basic intersection cohomology $\\lau{\\IH}{*}{\\per{p}}{\\mf}$ is finite dimensional and verifies the Poincar\\'e Duality. This duality includes two well-known situations:\n  -- Poincar\\'e Duality for basic cohomology (the action $\\Phi$ is almost free).\n  -- Poincar\\'e Duality for intersection cohomology (the group $G$ is compact and connected)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401407","kind":"arxiv","version":4},"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"}