{"paper":{"title":"Margulis numbers and number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.NT"],"primary_cat":"math.DG","authors_text":"Peter B. Shalen","submitted_at":"2009-02-06T04:23:12Z","abstract_excerpt":"It is shown that, up to isometry, all but finitely many closed, orientable hyperbolic 3-manifolds with a given trace field $K$ admit 0.34 as a Margulis number. This is deduced from a more technical result giving a condition under which $\\max(d(P,x\\cdot P),d(P,y\\cdot P))\\ge0.34$ for every $P\\in\\HH^3$, where $x$ and $y$ lie in $\\pizzle(E)$ for some number field $E$, generate a discrete torsion-free group of $\\pizzle(\\CC)$ and do not commute. Specifically, this is always the case if there is a valuation $v$ of $E$ such that (1) the residue field $k_v=\\frako_v/\\frakm_v$ of $v$ has sufficiently lar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1011","kind":"arxiv","version":2},"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"}