{"paper":{"title":"Slope detection, foliations in graph manifolds, and L-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Adam Clay, Steven Boyer","submitted_at":"2015-10-08T15:58:41Z","abstract_excerpt":"A graph manifold rational homology $3$-sphere $W$ with a left-orderable fundamental group admits a co-oriented taut foliation, though it is unknown whether it admits a smooth co-oriented taut foliation. In this paper we extend the gluing theorem of arXiv:1401.7726 to graph manifold rational homology solid tori and use this to show that there are smooth foliations on the pieces of $W$ which come close to matching up on its JSJ tori. This is applied to prove that a graph manifold with left-orderable fundamental group is not an L-space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02378","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":""},"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"}