{"paper":{"title":"Mapping class groups of circle bundles over a surface","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Bena Tshishiku, Lei Chen","submitted_at":"2023-01-13T03:16:30Z","abstract_excerpt":"In this paper, we study the algebraic structure of mapping class group $Mod(X)$ of 3-manifolds $X$ that fiber as a circle bundle over a surface $S^1\\rightarrow X\\rightarrow S_g$. There is an exact sequence $1\\rightarrow H^1(S_g)\\rightarrow Mod(X)\\rightarrow Mod(S_g)\\rightarrow1$. We relate this to the Birman exact sequence and determine when this sequence splits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.05375","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.05375/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"}