{"paper":{"title":"Small Sets of Topological Generators for Big Mapping Class Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Celal Can Bellek, Emir G\\\"ul, Mehmetcik Pamuk, O\\u{g}uz Y{\\i}ld{\\i}z, T\\\"ulin Altun\\\"oz","submitted_at":"2025-12-19T11:29:27Z","abstract_excerpt":"Let $S(n)$ be the infinite-type surface with infinite genus and $n \\in \\mathbb{N}$ ends, all of which are accumulated by genus. The mapping class group of this surface, $\\mathrm{Map}(S(n))$, is a Polish group that is not countably generated, but it is countably topologically generated. This paper focuses on finding minimal sets of generators for $\\mathrm{Map}(S(n))$. We show that for $n \\ge 8$, $\\mathrm{Map}(S(n))$ is topologically generated by three elements, and for $n \\ge 3$, it is topologically generated by four elements. We also establish a generating set of two elements for the Loch Ness"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.17465","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.17465/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}