{"paper":{"title":"A tightness criterion for homology manifolds with or without boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bhaskar Bagchi","submitted_at":"2014-06-17T10:06:20Z","abstract_excerpt":"A simplicial complex $X$ is said to be tight with respect to a field $\\mathbb{F}$ if $X$ is connected and, for every induced subcomplex $Y$ of $X$, the linear map $H_\\ast (Y; \\mathbb{F}) \\rightarrow H_\\ast (X; \\mathbb{F})$ (induced by the inclusion map) is injective. This notion was introduced by K\\\"{u}hnel in [10]. In this paper we prove the following two combinatorial criteria for tightness. (a) Any $(k+1)$-neighbourly $k$-stacked $\\mathbb{F}$-homology manifold with boundary is $\\mathbb{F}$-tight. Also, (b) any $\\mathbb{F}$-orientable $(k+1)$-neighbourly $k$-stacked $\\mathbb{F}$-homology man"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4299","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"}