{"paper":{"title":"A triangulation of $\\CC P^3$ as symmetric cube of $S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Basudeb Datta, Bhaskar Bagchi","submitted_at":"2010-12-15T06:42:31Z","abstract_excerpt":"The symmetric group $S_3$ acts on $S^2 \\times S^2 \\times S^2$ by coordinate permutation, and the quotient space $(S^2 \\times S^2 \\times S^2)/S_3$ is homeomorphic to the complex projective space $\\CC P^3$. In this paper, we construct an 124-vertex simplicial subdivision $(S^2 \\times S^2 \\times S^2)_{124}$ of the 64-vertex standard cellulation $S^2_4 \\times S^2_4 \\times S^2_4$ of $S^2 \\times S^2 \\times S^2$, such that the $S_3$-action on this cellulation naturally extends to an action on $(S^2 \\times S^2 \\times S^2)_{124}$. Further, the $S_3$-action on $(S^2 \\times S^2 \\times S^2)_{124}$ is \"goo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3235","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"}