{"paper":{"title":"$Z_2$-bordism and the Borsuk-Ulam Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Alice K. M. Libardi, Daciberg L. Goncalves, Michael C. Crabb, Pedro L. Q. Pergher","submitted_at":"2015-04-15T14:35:23Z","abstract_excerpt":"The purpose of this work is to classify, for given integers $m,\\, n\\geq 1$, the bordism class of a closed smooth $m$-manifold $X$ with a free smooth involution $\\tau$ with respect to the validity of the {\\it Borsuk-Ulam property} that for every continuous map $\\phi : X \\to R^n$ there exists a point $x\\in X$ such that $\\phi (x)=\\phi (\\tau (x))$. We will classify a given free $Z_2$-bordism class $\\alpha$ according to the three possible cases that (a) all representatives $(X , \\tau)$ of $\\alpha$ satisfy the Borsuk-Ulam property; \\ (b) there are representatives $(X_ 1, \\tau_1)$ and $(X_2, \\tau_2)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03929","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"}