{"paper":{"title":"The RAAGs on the complement graphs of path graphs in mapping class groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Erika Kuno, Takuya Katayama","submitted_at":"2018-04-10T12:06:53Z","abstract_excerpt":"In this article, we determine the function $\\ell(S_{g, p})$ such that the right-angled Artin group $G(P_{m})$ is embedded in the mapping class group $\\mathrm{Mod}(S_{g, p})$ if and only if $m$ is not more than $\\ell(S_{g, p})$. Using this function and Birman--Hilden theory, we prove that $\\mathrm{Mod}(S_{0, p})$ is virtually embedded in $\\mathrm{Mod}(S_{g, 0})$ if and only if $p \\leq 2g+2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03470","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":""},"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"}