{"paper":{"title":"Pseudo-Anosovs optimizing the ratio of Teichm\\\"uller to curve graph translation length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Samuel J. Taylor, Tarik Aougab","submitted_at":"2015-10-04T23:07:21Z","abstract_excerpt":"Given $\\phi$ a pseudo-Anosov map, let $\\ell_\\mathcal{T}(\\phi)$ denote the translation length of $\\phi$ in the Teichm\\\"uller space, and let $\\ell_\\mathcal{C}(\\phi)$ denote the stable translation length of $\\phi$ in the curve graph. Gadre--Hironaka--Kent--Leininger showed that, as a function of Euler characteristic $\\chi(S)$, the minimal possible ratio $\\tau(\\phi) = \\frac{\\ell_\\mathcal{T}(\\phi)}{\\ell_\\mathcal{C}(\\phi)}$ is $\\log(|\\chi(S)|)$, up to uniform additive and multiplicative constants. In this short note, we introduce a new construction of such ratio optimizers and demonstrate their abun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00995","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"}