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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.00397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-01T12:04:42Z","cross_cats_sorted":[],"title_canon_sha256":"dc0c199a23bd0a4e9f4b60f2cd871a5c3fa4a5a3072a107bf7fdbdb33c267536","abstract_canon_sha256":"48628b3972e6290e5cc9f625d2fd527e3d6a52b803acb613f8e396f4268de528"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:11.850863Z","signature_b64":"+CQbPb/TW+fjYgMqFmmZMi2P8B3SQHkCIw8FLjRHqxZ/f8YtiAWowjShIiT2IMrBM7s5a+iat2e9umrmFvB4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"445af3e610b59f7b54f1c99ebfa50f56cb23efbf2c5ce791e6556a4d966a1ccd","last_reissued_at":"2026-05-18T01:10:11.850159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:11.850159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\\\tau$. 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