{"paper":{"title":"Arbitrarily Long Factorizations in Mapping Class Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Elif Dalyan, Mehmetcik Pamuk, Mustafa Korkmaz","submitted_at":"2013-09-15T16:55:34Z","abstract_excerpt":"On a compact oriented surface of genus $g$ with $n\\geq 1$ boundary components, $\\delta_1, \\delta_2,\\ldots, \\delta_n$, we consider positive factorizations of the boundary multitwist $t_{\\delta_1} t_{\\delta_2} \\cdots t_{\\delta_n}$, where $t_{\\delta_i}$ is the positive Dehn twist about the boundary $\\delta_i$. We prove that for $g\\geq 3$, the boundary multitwist $t_{\\delta_1} t_{\\delta_2}$ can be written as a product of arbitrarily large number of positive Dehn twists about nonseparating simple closed curves, extending a recent result of Baykur and Van Horn-Morris, who proved this result for $g\\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3778","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"}