{"paper":{"title":"Embedding compact surfaces into the 3-dimensional Euclidean space 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":"2017-02-10T07:49:47Z","abstract_excerpt":"The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space $\\mathbb{R}^3$ are easier to feel by human's intuition. We give the maximum order of finite group actions on $(\\mathbb{R}^3, \\Sigma)$ among all possible embedded closed/bordered surfaces with given geometric/algebraic genus $>1$ in $\\mathbb{R}^3$. We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03087","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"}