{"paper":{"title":"On left-orderable fundamental groups and Dehn surgeries on twist knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anh T. Tran","submitted_at":"2013-01-04T03:38:21Z","abstract_excerpt":"We show that the resulting manifold by $r$-surgery on the hyperbolic twist knot $K_m, \\, m \\ge 2$, has left-orderable fundamental group if the slope $r$ satisfies the condition $r \\in (-4,2m)$ if $m$ is even, and $r \\in [0,4] \\cup (\\frac{4m}{\\omega}+4, 2m+4)$ if $m$ is odd, where $\\omega>1$ is the unique real solution of the equation $x e^{x}=4m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0665","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"}