{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3AHAFFRI723V77MA5ZT5SUYYAO","short_pith_number":"pith:3AHAFFRI","schema_version":"1.0","canonical_sha256":"d80e029628feb75ffd80ee67d95318038902808e825f7254262c6fffecdbe1d6","source":{"kind":"arxiv","id":"1806.09470","version":3},"attestation_state":"computed","paper":{"title":"A spectral sequence for Dehn fillings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Oliver H. Wang","submitted_at":"2018-06-25T14:04:37Z","abstract_excerpt":"We study how the cohomology of a type $F_\\infty$ relatively hyperbolic group pair $(G,\\mathcal{P})$ changes under Dehn fillings (i.e. quotients of group pairs). For sufficiently long Dehn fillings where the quotient pair $(\\bar{G},\\bar{\\mathcal{P}})$ is of type $F_\\infty$, we show that there is a spectral sequence relating the cohomology groups $H^i(G,\\mathcal{P};\\mathbb{Z} G)$ and $H^i\\left(\\bar{G},\\bar{\\mathcal{P}};\\mathbb{Z}\\bar{G}\\right)$. As a consequence, we show that essential cohomological dimension does not increase under these Dehn fillings."},"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":"1806.09470","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-25T14:04:37Z","cross_cats_sorted":[],"title_canon_sha256":"3cf7e7fb0c7242180593d2cf9e71ccf7ee76bc8c7e324cef0e94868a70245503","abstract_canon_sha256":"77f5f5c953bef8b0a7842c1b57c9193b4f8d014cf2f4c37b412710b65596ceed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:30:28.417097Z","signature_b64":"lwibwuLVdb9LwNSt1t91iv45ZHuTdwerm7L5Gm8AxBe7J1ZvjJQO7TwPupsKdEeYaVzJSGUaRahf2AE7GYviAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d80e029628feb75ffd80ee67d95318038902808e825f7254262c6fffecdbe1d6","last_reissued_at":"2026-07-05T03:30:28.416694Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:30:28.416694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A spectral sequence for Dehn fillings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Oliver H. Wang","submitted_at":"2018-06-25T14:04:37Z","abstract_excerpt":"We study how the cohomology of a type $F_\\infty$ relatively hyperbolic group pair $(G,\\mathcal{P})$ changes under Dehn fillings (i.e. quotients of group pairs). For sufficiently long Dehn fillings where the quotient pair $(\\bar{G},\\bar{\\mathcal{P}})$ is of type $F_\\infty$, we show that there is a spectral sequence relating the cohomology groups $H^i(G,\\mathcal{P};\\mathbb{Z} G)$ and $H^i\\left(\\bar{G},\\bar{\\mathcal{P}};\\mathbb{Z}\\bar{G}\\right)$. As a consequence, we show that essential cohomological dimension does not increase under these Dehn fillings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09470","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1806.09470/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1806.09470","created_at":"2026-07-05T03:30:28.416753+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.09470v3","created_at":"2026-07-05T03:30:28.416753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09470","created_at":"2026-07-05T03:30:28.416753+00:00"},{"alias_kind":"pith_short_12","alias_value":"3AHAFFRI723V","created_at":"2026-07-05T03:30:28.416753+00:00"},{"alias_kind":"pith_short_16","alias_value":"3AHAFFRI723V77MA","created_at":"2026-07-05T03:30:28.416753+00:00"},{"alias_kind":"pith_short_8","alias_value":"3AHAFFRI","created_at":"2026-07-05T03:30:28.416753+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01290","citing_title":"Cohomology of group theoretic Dehn fillings II","ref_index":57,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3AHAFFRI723V77MA5ZT5SUYYAO","json":"https://pith.science/pith/3AHAFFRI723V77MA5ZT5SUYYAO.json","graph_json":"https://pith.science/api/pith-number/3AHAFFRI723V77MA5ZT5SUYYAO/graph.json","events_json":"https://pith.science/api/pith-number/3AHAFFRI723V77MA5ZT5SUYYAO/events.json","paper":"https://pith.science/paper/3AHAFFRI"},"agent_actions":{"view_html":"https://pith.science/pith/3AHAFFRI723V77MA5ZT5SUYYAO","download_json":"https://pith.science/pith/3AHAFFRI723V77MA5ZT5SUYYAO.json","view_paper":"https://pith.science/paper/3AHAFFRI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.09470&json=true","fetch_graph":"https://pith.science/api/pith-number/3AHAFFRI723V77MA5ZT5SUYYAO/graph.json","fetch_events":"https://pith.science/api/pith-number/3AHAFFRI723V77MA5ZT5SUYYAO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3AHAFFRI723V77MA5ZT5SUYYAO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3AHAFFRI723V77MA5ZT5SUYYAO/action/storage_attestation","attest_author":"https://pith.science/pith/3AHAFFRI723V77MA5ZT5SUYYAO/action/author_attestation","sign_citation":"https://pith.science/pith/3AHAFFRI723V77MA5ZT5SUYYAO/action/citation_signature","submit_replication":"https://pith.science/pith/3AHAFFRI723V77MA5ZT5SUYYAO/action/replication_record"}},"created_at":"2026-07-05T03:30:28.416753+00:00","updated_at":"2026-07-05T03:30:28.416753+00:00"}