{"paper":{"title":"Surface mapping class group actions on 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alina Al Beaini, Bena Tshishiku, Lei Chen","submitted_at":"2023-11-27T03:08:08Z","abstract_excerpt":"For each circle bundle $S^1\\to X\\to\\Sigma_g$ over a surface with genus $g\\ge2$, there is a natural surjection $\\pi:Homeo^+(X)\\to Mod(\\Sigma_g)$. When $X$ is the unit tangent bundle $U\\Sigma_g$, it is well-known that $\\pi$ splits. On the other hand $\\pi$ does not split when the Euler number $e(X)$ is not divisible by the Euler characteristic $\\chi(\\Sigma_g)$ by work of the second two authors. In this paper we show that this homomorphism does not split in many cases where $\\chi(\\Sigma_g)$ divides $e(X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.15508","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/2311.15508/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"}