{"paper":{"title":"Traceless SU(2) representations of 2-stranded tangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Juanita Pinz\\'on-Caicedo, Paul Kirk, Yoshihiro Fukumoto","submitted_at":"2013-05-26T16:18:23Z","abstract_excerpt":"Given a 2-stranded tangle in a $\\ZZ/2$ homology ball, $T\\subset Y$, we investigate the character variety $R(Y,T)$ of conjugacy classes of traceless SU(2) representations of $\\pi_1(Y\\setminus T)$. In particular we completely determine the subspace of binary dihedral representations, and identify all of $R(Y,T)$ for many tangles naturally associated to knots in S^3. Moreover, we determine the image of the restriction map from $R(T,Y)$ to the traceless SU(2) character variety of the 4-punctured 2-sphere (the {\\it pillowcase}). We give examples to show this image can be non-linear in general, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6042","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"}