{"paper":{"title":"Whitney functions determine the real homotopy type of a semi-analytic set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AT","authors_text":"Bryce Chriestenson, Markus J. Pflaum","submitted_at":"2014-03-07T00:49:34Z","abstract_excerpt":"In this paper, we investigate the Whitney--de Rham complex $\\Omega^\\bullet_\\text{W} (X)$ associated to a semi-analytic subset $X$ of an analytic manifold $M$. This complex is a commutative differential graded algebra, that is defined to be the quotient of the de Rham complex of smooth differential forms on $M$ by the differential graded ideal generated by all smooth functions which are flat on $X$. We use Hironaka's desingularization theorem to prove a Poincar\\'e Lemma for $\\Omega^\\bullet_\\text{W} (X)$ holds true, which entails that its cohomology is isomorphic to the real cohomology of $X$. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1627","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"}