{"paper":{"title":"Virtually Haken surgeries on once-punctured torus bundles","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Joseph D. Masters","submitted_at":"2005-06-22T16:15:22Z","abstract_excerpt":"We describe a class $\\mathcal{C}$ of punctured torus bundles such that, for each $M \\in \\mathcal{C}$, all but finitely many Dehn fillings on $M$ are virtually Haken.\n We show that $\\mathcal{C}$ contains infinitely many commensurability classes, and we give evidence that $\\mathcal{C}$ includes representatives of ``most'' commensurability classes of punctured torus bundles.\n In particular, we define an integer-valued complexity function on monodromies $f$ (essentially the length of the LR-factorization of $f_*$ in $PSL_2(\\mathbb{Z})$), and use a computer to show that if the monodromy of $M$ has "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506443","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":""},"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"}