{"paper":{"title":"Combinatorial triangulations of homology spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Basudeb Datta, Bhaskar Bagchi","submitted_at":"2005-06-27T11:16:42Z","abstract_excerpt":"Let $M$ be an $n$-vertex combinatorial triangulation of a $\\ZZ_2$-homology $d$-sphere. In this paper we prove that if $n \\leq d + 8$ then $M$ must be a combinatorial sphere. Further, if $n = d + 9$ and $M$ is not a combinatorial sphere then $M$ can not admit any proper bistellar move. Existence of a 12-vertex triangulation of the lens space $L(3, 1)$ shows that the first result is sharp in dimension three.\n  In the course of the proof we also show that any $\\ZZ_2$-acyclic simplicial complex on $\\leq 7$ vertices is necessarily collapsible. This result is best possible since there exist 8-vertex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506536","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"}