{"paper":{"title":"Lifting curves simply","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jonah Gaster","submitted_at":"2015-01-01T18:09:27Z","abstract_excerpt":"We provide linear lower bounds for $f_\\rho(L)$, the smallest integer so that every curve on a fixed hyperbolic surface $(S,\\rho)$ of length at most $L$ lifts to a simple curve on a cover of degree at most $f_\\rho(L)$. This bound is independent of hyperbolic structure $\\rho$, and improves on a recent bound of Gupta-Kapovich. When $(S,\\rho)$ is without punctures, using work of Patel we conclude asymptotically linear growth of $f_\\rho$. When $(S,\\rho)$ has a puncture, we obtain exponential lower bounds for $f_\\rho$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00295","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"}