{"paper":{"title":"Small filling sets of curves on a surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alexandra Pettet, Hugo Parlier, James W. Anderson","submitted_at":"2009-09-10T15:06:53Z","abstract_excerpt":"We show that the asymptotic growth rate for the minimal cardinality of a set of simple closed curves on a closed surface of genus $g$ which fill and pairwise intersect at most $K\\ge 1$ times is $2\\sqrt{g}/\\sqrt{K}$ as $g \\to \\infty$ . We then bound from below the cardinality of a filling set of systoles by $g/\\log(g)$. This illustrates that the topological condition that a set of curves pairwise intersect at most once is quite far from the geometric condition that such a set of curves can arise as systoles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1966","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"}