{"paper":{"title":"Graphs in the 3--sphere with maximum symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bruno Zimmermann, Chao Wang, Shicheng Wang, Yimu Zhang","submitted_at":"2015-10-03T13:47:44Z","abstract_excerpt":"We consider the orientation-preserving actions of finite groups $G$ on pairs $(S^3, \\Gamma)$, where $\\Gamma$ is a connected graph of genus $g>1$, embedded in $S^3$. For each $g$ we give the maximum order $m_g$ of such $G$ acting on $(S^3, \\Gamma)$ for all such $\\Gamma\\subset S^3$. Indeed we will classify all graphs $\\Gamma\\subset S^3$ which realize these $m_g$ in different levels: as abstract graphs and as spatial graphs, as well as their group actions.\n  Such maximum orders without the condition \"orientation-preserving\" are also addressed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00822","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"}