{"paper":{"title":"Poincar\\'e duality, Hilbert complexes and geometric applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francesco Bei","submitted_at":"2012-09-16T23:07:15Z","abstract_excerpt":"Let $(M,g)$ an open and oriented riemannian manifold. The aim of this paper is to study some properties of the two following sequences of $L^2$ cohomology groups: $H^i_{2,m\\rightarrow M}(M,g)$ defined as the image $\\im(H^i_{2,min}(M,g)\\rightarrow H^i_{2,max}(M,g))$ and $\\bar{H}^i_{2,m\\rightarrow M}(M,g)$ defined as $\\im(\\bar{H}^i_{2,min}(M,g)\\rightarrow \\bar{H}^i_{2,max}(M,g))$. We show, under certain hypothesis, that the first sequence is the cohomology of a suitable Hilbert complex which contains the minimal one and is contained in the maximal one. We also show that when the second sequence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3528","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"}