{"paper":{"title":"Real analytic lift of foliations of Thurston and Tsuboi","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Shigeyuki Morita, Teruaki Kitano, Yoshihiko Mitsumatsu","submitted_at":"2026-05-31T05:21:08Z","abstract_excerpt":"Thurston constructed codimension one foliations on $S^3$ thereby proved that the homomorphism $gv: \\pi_3(B\\overline{\\Gamma}^\\infty_1)\\rightarrow \\mathbb{R}$ induced by the Godbillon-Vey invariant is surjective. By another real analytic construction, he proved that the homomorphism $gv: H_3(B\\overline{\\Gamma}^\\omega_1)\\rightarrow \\mathbb{R}$ is also surjective where $B\\overline{\\Gamma}^\\omega_1$ is a $K(\\pi,1)$ space by Haefliger.\n  Tsuboi proved that the former surjection splits so that $\\pi_3(B\\overline{\\Gamma}^\\infty_1)= \\mathbb{R}\\oplus \\mathrm{Ker}\\,gv$. He further showed that the subgroup"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01017","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/2606.01017/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"}