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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 $(X_2, \\tau_2)$"},"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":"1504.03929","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-04-15T14:35:23Z","cross_cats_sorted":[],"title_canon_sha256":"9f670e9e240f38b6ff4af4ce9722576454e3ab095b12cb4f0ad25e367382e073","abstract_canon_sha256":"f1ae39906c6f7296dc17ca1c065a7c0ad7cccd9f980f24d15ff332cc4e755de2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:14.956784Z","signature_b64":"GUOM32nAqxhUtHJJGU1Mrl7Bk98dn2dFhhEPkRdgTRhoKuSKgiG4fjqGywekcO2HR0BD3wSv7WXcMc4lauELDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29da7ad4a62708d37b233486343cb0fb2afbe81135f9631cbfbb2ea19203d554","last_reissued_at":"2026-05-18T02:18:14.956288Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:14.956288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1504.03929","created_at":"2026-05-18T02:18:14.956361+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.03929v2","created_at":"2026-05-18T02:18:14.956361+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03929","created_at":"2026-05-18T02:18:14.956361+00:00"},{"alias_kind":"pith_short_12","alias_value":"FHNHVVFGE4EN","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FHNHVVFGE4ENG6ZD","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FHNHVVFG","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FHNHVVFGE4ENG6ZDGSDDIPFQ7M","json":"https://pith.science/pith/FHNHVVFGE4ENG6ZDGSDDIPFQ7M.json","graph_json":"https://pith.science/api/pith-number/FHNHVVFGE4ENG6ZDGSDDIPFQ7M/graph.json","events_json":"https://pith.science/api/pith-number/FHNHVVFGE4ENG6ZDGSDDIPFQ7M/events.json","paper":"https://pith.science/paper/FHNHVVFG"},"agent_actions":{"view_html":"https://pith.science/pith/FHNHVVFGE4ENG6ZDGSDDIPFQ7M","download_json":"https://pith.science/pith/FHNHVVFGE4ENG6ZDGSDDIPFQ7M.json","view_paper":"https://pith.science/paper/FHNHVVFG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.03929&json=true","fetch_graph":"https://pith.science/api/pith-number/FHNHVVFGE4ENG6ZDGSDDIPFQ7M/graph.json","fetch_events":"https://pith.science/api/pith-number/FHNHVVFGE4ENG6ZDGSDDIPFQ7M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FHNHVVFGE4ENG6ZDGSDDIPFQ7M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FHNHVVFGE4ENG6ZDGSDDIPFQ7M/action/storage_attestation","attest_author":"https://pith.science/pith/FHNHVVFGE4ENG6ZDGSDDIPFQ7M/action/author_attestation","sign_citation":"https://pith.science/pith/FHNHVVFGE4ENG6ZDGSDDIPFQ7M/action/citation_signature","submit_replication":"https://pith.science/pith/FHNHVVFGE4ENG6ZDGSDDIPFQ7M/action/replication_record"}},"created_at":"2026-05-18T02:18:14.956361+00:00","updated_at":"2026-05-18T02:18:14.956361+00:00"}