{"paper":{"title":"Geometric construction of bases of $H_2(\\overline\\Omega, \\partial\\Omega, \\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ana Alonso Rodr\\'iguez, Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna","submitted_at":"2016-07-18T14:27:19Z","abstract_excerpt":"We present an efficient algorithm for the construction of a basis of $H_2(\\overline{\\Omega},\\partial\\Omega;\\mathbb Z)$ via the Poincar\\'e--Lefschetz duality theorem. Denoting by $g$ the first Betti number of $\\overline \\Omega$ the idea is to find, first $g$ different $1$-boundaries of $\\overline{\\Omega}$ with supports contained in $\\partial\\Omega$ whose homology classes in $\\mathbb R^3 \\setminus \\Omega$ form a basis of $H_1(\\mathbb R^3 \\setminus \\Omega;\\mathbb Z)$, and then to construct in $\\overline{\\Omega}$ a homological Seifert surface of each one of these $1$-boundaries. The Poincar\\'e--Le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05099","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"}