{"paper":{"title":"Simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Donghi Lee, Makoto Sakuma","submitted_at":"2012-06-19T16:35:39Z","abstract_excerpt":"Following Riley's work, for each 2-bridge link $K(r)$ of slope $r\\in\\QQ$ and an integer or a half-integer $n$ greater than 1, we introduce the {\\it Heckoid orbifold $\\orbs(r;n)$} and the {\\it Heckoid group $\\Hecke(r;n)=\\pi_1(\\orbs(r;n))$ of index $n$ for $K(r)$}. When $n$ is an integer, $\\orbs(r;n)$ is called an {\\it even} Heckoid orbifold; in this case, the underlying space is the exterior of $K(r)$, and the singular set is the lower tunnel of $K(r)$ with index $n$. The main purpose of this note is to announce answers to the following questions for even Heckoid orbifolds. (1) For an essential"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4258","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"}