{"paper":{"title":"Sparse Filtered Nerves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Morten Brun, Nello Blaser","submitted_at":"2018-10-04T11:29:42Z","abstract_excerpt":"Given a point cloud $P$ in Euclidean space and a positive parameter $t$ we can consider the $t$-neighborhood $P^{t}$ of $P$ consisting of points at distance less than $t$ to $P$. Homology of $P^{t}$ gives information about components, holes, voids etc. in $P^{t}$. The idea of persistent homology is that it may happen that we are interested in some of holes in the spaces $P^t$ that are not detected simultaneously in homology for a single value of $t$, but where each of these holes is detected for $t$ in a wide range.\n  When the dimension of the ambient Euclidean space is small, persistent homol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02149","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"}