{"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"}