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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.4299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-06-17T10:06:20Z","cross_cats_sorted":[],"title_canon_sha256":"26474216854f8c6ccdfbb427699f80c89849ee35cbfdc17b434dffb4e4954bbb","abstract_canon_sha256":"c5e59484ee63b84f8acc3b721187448f776dbf8f5f4509c0cd848168678d6666"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:37.907868Z","signature_b64":"xMlnrL8QIeUcHPoFHduiOZZNHV5xxdr2c4t2terHQVyC9AlDTLL66PKsAAGJJqyEkGWmcjULFMiOYLjKErZZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7c503a7e2d34a2585745139b03d08c232bd62b73ce910394206030977d0f101","last_reissued_at":"2026-05-18T02:49:37.907428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:37.907428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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