{"paper":{"title":"Small asymptotic translation lengths of pseudo-Anosov maps on the curve complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eiko Kin, Hyunshik Shin","submitted_at":"2017-07-19T08:59:14Z","abstract_excerpt":"Let $M$ be a hyperbolic fibered 3-manifold with $b_1(M) \\geq 2$ and let $S$ be a fiber with pseudo-Anosov monodromy $\\psi$. We show that there exists a sequence $(R_n, \\psi_n)$ of fibers and monodromies contained in the fibered cone of $(S,\\psi)$ such that the asymptotic translation length of $\\psi_n$ on the curve complex $\\mathcal{C}(R_n)$ behaves asymptotically like $1/|\\chi(R_n)|^2$. As applications, we can reprove the previous result by Gadre--Tsai that the minimal asymptotic translation length of a closed surface of genus $g$ asymptotically behaves like $1/g^2$. We also show that this als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05983","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"}