{"paper":{"title":"On the traceless SU(2) character variety of the 6-punctured 2-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Paul Kirk","submitted_at":"2015-12-31T19:13:17Z","abstract_excerpt":"We exhibit the traceless $SU(2)$ character variety of a 6-punctured 2-sphere as a 2-fold branched cover of ${\\mathbb{C}}P^3$, branched over the singular Kummer surface, with the branch locus in $R(S^2,6)$ corresponding to the binary dihedral representations. This follows from an analysis of the map induced on $SU(2)$ character varieties by the 2-fold branched cover $F_{n-1}\\to S^2$ branched over $2n$ points, combined with the theorem of Narasimhan-Ramanan which identifies $R(F_2)$ with ${\\mathbb{C}} P^3$. The singular points of $R(S^2,6)$ correspond to abelian representations, and we prove tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09345","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"}