{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GMXDXU6TVC7RW3ATBF5ZVBANM5","short_pith_number":"pith:GMXDXU6T","schema_version":"1.0","canonical_sha256":"332e3bd3d3a8bf1b6c13097b9a840d67534ff1e1f946ab1015d5c5f336ba4185","source":{"kind":"arxiv","id":"1309.0043","version":1},"attestation_state":"computed","paper":{"title":"Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Grigori Avramidi, T. Tam Nguyen Phan, Yunhui Wu","submitted_at":"2013-08-30T22:49:25Z","abstract_excerpt":"We study noncompact, complete, finite volume, Riemannian 4-manifolds $M$ with sectional curvature $-1<K<0$. We prove that $\\pi_1 M$ cannot be a 3-manifold group. A classical theorem of Gromov says that $M$ is homeomorphic to the interior of a compact manifold $\\M$ with boundary $\\partial\\barM$. We show that for each $\\pi_1$-injective boundary component $C$ of $\\M$, the map $i_*$ induced by inclusion $i\\colon C\\rightarrow \\M$ has infinite index image $i_*(\\pi_1 C)$ in $\\pi_1 \\M$. We also prove that $M$ cannot be homotoped to be contained in $\\partial\\M$."},"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":"1309.0043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-30T22:49:25Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"81beadf14ca46348b008337fbada43ab046f5aab087855b5723c09174a676541","abstract_canon_sha256":"a86da413b6ea4fc504fd299cf96b057cf97f516fffb4329baf057ac5321f7486"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:28.978912Z","signature_b64":"NENIe7MSc0pKLn9m0Me9CRGt4Hcb6yXw8imshxTaFLyQcBBuzZxV56vP5QUuj8VcyXIfmETdDUSst9lfdvJAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"332e3bd3d3a8bf1b6c13097b9a840d67534ff1e1f946ab1015d5c5f336ba4185","last_reissued_at":"2026-05-18T03:14:28.978428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:28.978428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Grigori Avramidi, T. Tam Nguyen Phan, Yunhui Wu","submitted_at":"2013-08-30T22:49:25Z","abstract_excerpt":"We study noncompact, complete, finite volume, Riemannian 4-manifolds $M$ with sectional curvature $-1<K<0$. We prove that $\\pi_1 M$ cannot be a 3-manifold group. A classical theorem of Gromov says that $M$ is homeomorphic to the interior of a compact manifold $\\M$ with boundary $\\partial\\barM$. We show that for each $\\pi_1$-injective boundary component $C$ of $\\M$, the map $i_*$ induced by inclusion $i\\colon C\\rightarrow \\M$ has infinite index image $i_*(\\pi_1 C)$ in $\\pi_1 \\M$. We also prove that $M$ cannot be homotoped to be contained in $\\partial\\M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0043","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1309.0043","created_at":"2026-05-18T03:14:28.978503+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0043v1","created_at":"2026-05-18T03:14:28.978503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0043","created_at":"2026-05-18T03:14:28.978503+00:00"},{"alias_kind":"pith_short_12","alias_value":"GMXDXU6TVC7R","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GMXDXU6TVC7RW3AT","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GMXDXU6T","created_at":"2026-05-18T12:27:45.050594+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/GMXDXU6TVC7RW3ATBF5ZVBANM5","json":"https://pith.science/pith/GMXDXU6TVC7RW3ATBF5ZVBANM5.json","graph_json":"https://pith.science/api/pith-number/GMXDXU6TVC7RW3ATBF5ZVBANM5/graph.json","events_json":"https://pith.science/api/pith-number/GMXDXU6TVC7RW3ATBF5ZVBANM5/events.json","paper":"https://pith.science/paper/GMXDXU6T"},"agent_actions":{"view_html":"https://pith.science/pith/GMXDXU6TVC7RW3ATBF5ZVBANM5","download_json":"https://pith.science/pith/GMXDXU6TVC7RW3ATBF5ZVBANM5.json","view_paper":"https://pith.science/paper/GMXDXU6T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0043&json=true","fetch_graph":"https://pith.science/api/pith-number/GMXDXU6TVC7RW3ATBF5ZVBANM5/graph.json","fetch_events":"https://pith.science/api/pith-number/GMXDXU6TVC7RW3ATBF5ZVBANM5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GMXDXU6TVC7RW3ATBF5ZVBANM5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GMXDXU6TVC7RW3ATBF5ZVBANM5/action/storage_attestation","attest_author":"https://pith.science/pith/GMXDXU6TVC7RW3ATBF5ZVBANM5/action/author_attestation","sign_citation":"https://pith.science/pith/GMXDXU6TVC7RW3ATBF5ZVBANM5/action/citation_signature","submit_replication":"https://pith.science/pith/GMXDXU6TVC7RW3ATBF5ZVBANM5/action/replication_record"}},"created_at":"2026-05-18T03:14:28.978503+00:00","updated_at":"2026-05-18T03:14:28.978503+00:00"}