{"paper":{"title":"The most symmetric surfaces in the 3-torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Chao Wang, Sheng Bai, Shicheng Wang, Vanessa Robins","submitted_at":"2016-03-26T06:10:50Z","abstract_excerpt":"Suppose an orientation preserving action of a finite group $G$ on the closed surface $\\Sigma_g$ of genus $g>1$ extends over the 3-torus $T^3$ for some embedding $\\Sigma_g\\subset T^3$. Then $|G|\\le 12(g-1)$, and this upper bound $12(g-1)$ can be achieved for $g=n^2+1, 3n^2+1, 2n^3+1, 4n^3+1, 8n^3+1, n\\in \\mathbb{Z}_+$. Those surfaces in $T^3$ realizing the maximum symmetries can be either unknotted or knotted. Similar problems in non-orientable category is also discussed.\n  Connection with minimal surfaces in $T^3$ is addressed and when the maximum symmetric surfaces above can be realized by mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08077","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"}