{"paper":{"title":"Filling systems on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bidyut Sanki, Shiv Parsad","submitted_at":"2017-08-23T09:20:46Z","abstract_excerpt":"Let $F_g$ be a closed orientable surface of genus $g$. A set $\\Omega = \\{ \\gamma_1, \\dots, \\gamma_s\\}$ of pairwise non-homotopic simple closed curves on $F_g$ is called a \\emph{filling system} or simply a \\emph{filling} of $F_g$, if $F_g\\setminus \\Omega$ is a union of $b$ topological discs for some $b\\geq 1$. A filling system is called \\emph{minimal}, if $b=1$. The \\emph{size} of a filling is defined as the number of its elements. We prove that the maximum size of a filling of $F_g$ with $b$ complementary discs is $2g+b-1$. Next, we show that for $g\\geq 2, b\\geq 1\\text{ with }(g,b)\\neq (2,1)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06928","kind":"arxiv","version":4},"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"}