{"paper":{"title":"The Borsuk-Ulam property for homotopy classes of selfmaps of surfaces of Euler characteristic zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daciberg Lima Gon\\c{c}alves (IME), John Guaschi (LMNO), Vinicius Casteluber Laass","submitted_at":"2016-08-01T12:04:42Z","abstract_excerpt":"Let M and N be topological spaces such that M admits a free involution $\\\\tau$. A homotopy class $\\beta$ $\\in$ [M, N ] is said to have the Borsuk-Ulam property with respect to $\\\\tau$ if for every representative map f : M $\\rightarrow$ N of $\\beta$, there exists a point x $\\in$ M such that f ($\\\\tau$ (x)) = f (x). In the case where M is a compact, connected manifold without boundary and N is a compact, connected surface without boundary different from the 2-sphere and the real projective plane, we formulate this property in terms of the pure and full 2-string braid groups of N , and of the fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00397","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"}