{"paper":{"title":"Path lifting properties and embedding between RAAGs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eon-Kyung Lee, Sang-Jin Lee","submitted_at":"2015-07-24T14:32:02Z","abstract_excerpt":"For a finite simplicial graph $\\Gamma$, let $G(\\Gamma)$ denote the right-angled Artin group on the complement graph of $\\Gamma$. In this article, we introduce the notions of \"induced path lifting property\" and \"semi-induced path lifting property\" for immersions between graphs, and obtain graph theoretical criteria for the embedability between right-angled Artin groups. We recover the result of S.-h.{} Kim and T.{} Koberda that an arbitrary $G(\\Gamma)$ admits a quasi-isometric group embedding into $G(T)$ for some finite tree $T$. The upper bound on the number of vertices of $T$ is improved from"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06859","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"}