{"paper":{"title":"Centrally symmetric manifolds with few vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Isabella Novik, Steven Klee","submitted_at":"2011-02-02T20:09:33Z","abstract_excerpt":"A centrally symmetric $2d$-vertex combinatorial triangulation of the product of spheres $\\S^i\\times\\S^{d-2-i}$ is constructed for all pairs of non-negative integers $i$ and $d$ with $0\\leq i \\leq d-2$. For the case of $i=d-2-i$, the existence of such a triangulation was conjectured by Sparla. The constructed complex admits a vertex-transitive action by a group of order $4d$. The crux of this construction is a definition of a certain full-dimensional subcomplex, $\\B(i,d)$, of the boundary complex of the $d$-dimensional cross-polytope. This complex $\\B(i,d)$ is a combinatorial manifold with boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0542","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"}