{"paper":{"title":"Noncommutative Chern-Simons theory on the quantum 3-sphere $S^3_\\theta$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Dan Li","submitted_at":"2013-10-27T19:13:13Z","abstract_excerpt":"We consider the $\\theta$-deformed quantum three sphere $S^3_\\theta$ and study its Chern--Simons theory from a spectral point of view. We first construct a spectral triple on $S^3_\\theta$ as a generalization of the Dirac geometry on $S^3 $. Since the choice of Dirac operator is not unique, we give two more natural spectral triples on $S^3_\\theta$ related to the standard round metric. We then compute the Chern--Simons action with respect to the three spectral triples, it turns out that it is not a topological invariant, that is, it depends on the choice of Dirac operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7233","kind":"arxiv","version":4},"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"}