{"paper":{"title":"On malnormal peripheral subgroups in fundamental groups of 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Claude Weber, Pierre de la Harpe","submitted_at":"2011-04-15T14:06:10Z","abstract_excerpt":"Let $K$ be a non-trivial knot in the 3-sphere, $E_K$ its exterior, $G_K = \\pi_1(E_K)$ its group, and $P_K = \\pi_1(\\partial E_K) \\subset G_K$ its peripheral subgroup. We show that $P_K$ is malnormal in $G_K$, namely that $gP_Kg^{-1} \\cap P_K = \\{e\\}$ for any $g \\in G_K$ with $g \\notin P_K$, unless $K$ is in one of the following three classes: torus knots, cable knots, and composite knots; these are exactly the classes for which there exist annuli in $E_K$ attached to $T_K$ which are not boundary parallel (Theorem 1 and Corollary 2). More generally, we characterise malnormal peripheral subgroups"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3062","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"}