{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YF5AUQGSSLMO6DQOJTS773LWTF","short_pith_number":"pith:YF5AUQGS","schema_version":"1.0","canonical_sha256":"c17a0a40d292d8ef0e0e4ce5ffed769942ad3950167f3687cb8b97e3ef42eaf2","source":{"kind":"arxiv","id":"1310.6565","version":4},"attestation_state":"computed","paper":{"title":"Finite group actions on manifolds without odd cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DG","authors_text":"Ignasi Mundet i Riera","submitted_at":"2013-10-24T11:09:24Z","abstract_excerpt":"Let $X$ be a compact smooth manifold, possibly with boundary. Denote by $X_1,\\dots,X_r$ the connected components of $X$. Assume that the integral cohomology of $X$ is torsion free and supported in even degrees. We prove that there exists a constant $C$ such that any finite group $G$ acting smoothly and effectively on $X$ has an abelian subgroup $A$ of index at most $C$, which can be generated by at most $\\sum_i[\\dim X_i/2]$ elements, and which satisfies $\\chi(X_i^A)=\\chi(X_i)$ for every $i$. This proves, for all such manifolds $X$, a conjecture of \\'Etienne Ghys. An essential ingredient of the"},"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":"1310.6565","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-24T11:09:24Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"e637f4b37df9c945c3ba61b078281897044218941382025dd42747238ec4182d","abstract_canon_sha256":"6aa3057276002acc1fdadb69596f3f01623544b22886b25d2780449c1e8f52a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:51.750858Z","signature_b64":"r1VZVAclil0YWk28T190XFUGI+DtaHmFgrFZdz99rhwOWANcybP3sWDDc984L+xMqE/4SiltlAqHpMfKanPIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c17a0a40d292d8ef0e0e4ce5ffed769942ad3950167f3687cb8b97e3ef42eaf2","last_reissued_at":"2026-05-18T02:50:51.750390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:51.750390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite group actions on manifolds without odd cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DG","authors_text":"Ignasi Mundet i Riera","submitted_at":"2013-10-24T11:09:24Z","abstract_excerpt":"Let $X$ be a compact smooth manifold, possibly with boundary. Denote by $X_1,\\dots,X_r$ the connected components of $X$. Assume that the integral cohomology of $X$ is torsion free and supported in even degrees. We prove that there exists a constant $C$ such that any finite group $G$ acting smoothly and effectively on $X$ has an abelian subgroup $A$ of index at most $C$, which can be generated by at most $\\sum_i[\\dim X_i/2]$ elements, and which satisfies $\\chi(X_i^A)=\\chi(X_i)$ for every $i$. This proves, for all such manifolds $X$, a conjecture of \\'Etienne Ghys. An essential ingredient of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6565","kind":"arxiv","version":4},"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":"1310.6565","created_at":"2026-05-18T02:50:51.750458+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.6565v4","created_at":"2026-05-18T02:50:51.750458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6565","created_at":"2026-05-18T02:50:51.750458+00:00"},{"alias_kind":"pith_short_12","alias_value":"YF5AUQGSSLMO","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YF5AUQGSSLMO6DQO","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YF5AUQGS","created_at":"2026-05-18T12:28:06.772260+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/YF5AUQGSSLMO6DQOJTS773LWTF","json":"https://pith.science/pith/YF5AUQGSSLMO6DQOJTS773LWTF.json","graph_json":"https://pith.science/api/pith-number/YF5AUQGSSLMO6DQOJTS773LWTF/graph.json","events_json":"https://pith.science/api/pith-number/YF5AUQGSSLMO6DQOJTS773LWTF/events.json","paper":"https://pith.science/paper/YF5AUQGS"},"agent_actions":{"view_html":"https://pith.science/pith/YF5AUQGSSLMO6DQOJTS773LWTF","download_json":"https://pith.science/pith/YF5AUQGSSLMO6DQOJTS773LWTF.json","view_paper":"https://pith.science/paper/YF5AUQGS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.6565&json=true","fetch_graph":"https://pith.science/api/pith-number/YF5AUQGSSLMO6DQOJTS773LWTF/graph.json","fetch_events":"https://pith.science/api/pith-number/YF5AUQGSSLMO6DQOJTS773LWTF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YF5AUQGSSLMO6DQOJTS773LWTF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YF5AUQGSSLMO6DQOJTS773LWTF/action/storage_attestation","attest_author":"https://pith.science/pith/YF5AUQGSSLMO6DQOJTS773LWTF/action/author_attestation","sign_citation":"https://pith.science/pith/YF5AUQGSSLMO6DQOJTS773LWTF/action/citation_signature","submit_replication":"https://pith.science/pith/YF5AUQGSSLMO6DQOJTS773LWTF/action/replication_record"}},"created_at":"2026-05-18T02:50:51.750458+00:00","updated_at":"2026-05-18T02:50:51.750458+00:00"}