{"paper":{"title":"Embedding periodic maps on surfaces into those on $S^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Chao Wang, Shicheng Wang, Yimu Zhang, Yu Guo","submitted_at":"2013-02-05T09:34:45Z","abstract_excerpt":"Call a periodic map $h$ on the closed orientable surface $\\Sigma_g$ extendable if $h$ extends to a periodic map over the pair $(S^3, \\Sigma_g)$ for possible embeddings $e: \\Sigma_g\\to S^3$.\n  We determine the extendabilities for all periodical maps on $\\Sigma_2$. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair $(S^3, \\Sigma_g)$. To do this we first list all periodic maps on $\\Sigma_2$, and indeed we exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself shoul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0972","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"}