{"paper":{"title":"Congruence topologies on the mapping class group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GR","authors_text":"Marco Boggi","submitted_at":"2018-04-17T15:33:53Z","abstract_excerpt":"Let $\\Gamma(S)$ be the pure mapping class group of a connected orientable surface $S$ of negative Euler characteristic. For ${\\mathscr C}$ a class of finite groups, let $\\hat{\\pi}_1(S)^{\\mathscr C}$ be the pro-${\\mathscr C}$ completion of the fundamental group of $S$. The \\emph{${\\mathscr C}$-congruence completion $\\check{\\Gamma}(S)^{\\mathscr C}$ of $\\Gamma(S)$} is the profinite completion induced by the embedding $\\Gamma(S)\\hookrightarrow{\\operatorname{Out}}(\\hat{\\pi}_1(S)^{\\mathscr C})$. In this paper, we begin a systematic study of such completions for different ${\\mathscr C}$. We show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06322","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"}