{"paper":{"title":"Injective homomorphisms of mapping class groups of non-orientable surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Elmas Irmak, Luis Paris (IMB)","submitted_at":"2017-08-01T09:28:28Z","abstract_excerpt":"Let $N$ be a compact, connected, non-orientable surface of genus $\\rho$ with $n$ boundary components, with $\\rho \\ge 5$ and $n \\ge 0$, and let $\\mathcal{M} (N)$ be the mapping class group of $N$. We show that, if $\\mathcal{G}$ is a finite index subgroup of $\\mathcal{M} (N)$ and $\\varphi: \\mathcal{G} \\to \\mathcal{M}  (N)$ is an injective homomorphism, then there exists $f_0 \\in \\mathcal{M}  (N)$ such that $\\varphi (g) = f_0 g f_0^{-1}$ for all $g \\in \\mathcal{G}$. We deduce that the abstract commensurator of $\\mathcal{M}  (N)$ coincides with $\\mathcal{M}  (N)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00218","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"}