{"paper":{"title":"Cups Products in Z2-Cohomology of 3D Polyhedral Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Javier Lamar, Rocio Gonalez-Diaz, Ronald Umble","submitted_at":"2012-07-10T13:40:40Z","abstract_excerpt":"Let $I=(\\mathbb{Z}^3,26,6,B)$ be a 3D digital image, let $Q(I)$ be the associated cubical complex and let $\\partial Q(I)$ be the subcomplex of $Q(I)$ whose maximal cells are the quadrangles of $Q(I)$ shared by a voxel of $B$ in the foreground -- the object under study -- and by a voxel of $\\mathbb{Z}^3\\smallsetminus B$ in the background -- the ambient space. We show how to simplify the combinatorial structure of $\\partial Q(I)$ and obtain a 3D polyhedral complex $P(I)$ homeomorphic to $\\partial Q(I)$ but with fewer cells. We introduce an algorithm that computes cup products on $H^*(P(I);\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2346","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"}