{"paper":{"title":"The 27 possible intrinsic symmetry groups of two-component links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"James Cornish, Jason Cantarella, Jason Parsley, Matt Mastin","submitted_at":"2012-01-13T01:28:32Z","abstract_excerpt":"We consider the \"intrinsic\" symmetry group of a two-component link $L$, defined to be the image $\\Sigma(L)$ of the natural homomorphism from the standard symmetry group $\\MCG(S^3,L)$ to the product $\\MCG(S^3) \\cross \\MCG(L)$. This group, first defined by Whitten in 1969, records directly whether $L$ is isotopic to a link $L'$ obtained from $L$ by permuting components or reversing orientations; it is a subgroup of $\\Gamma_2$, the group of all such operations.\n  For two-component links, we catalog the 27 possible intrinsic symmetry groups, which represent the subgroups of $\\Gamma_2$ up to conjug"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2722","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"}