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It is known for every knot $K$ that if $K$ is fibered, then for every non-abelian representation, $\\Delta_{K,\\rho}$ is monic and has degree $4g(K)-2$ where $g(K)$ is the genus of $K$. Kim and Morifuji recently proved the converse for 2-bridge knots. In fact they proved a stronger result: if a 2-bridge knot $K$ is non-fibered, then all but finitely many non-abelian representations on some component have $\\Delta_{K,\\rho}$ non-monic and de"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.1631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-07T02:39:39Z","cross_cats_sorted":[],"title_canon_sha256":"efeba5688b01eeca1cfc1ddfd4a51ee9e5457c35f45a10bf74f99917daef183b","abstract_canon_sha256":"b1fb8658e53b3b7254bebc0e67d025d7a1f755e2e6816057f645b49bb3a79d0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:17.381628Z","signature_b64":"k3sqmNuT5l9YnFPqBYpy8vMgKoSc++CFcQ+thWFB1XUrwQAE6yFITBimAY0Zc/bqhaQFRXGNCn42j5pW3oDmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9aeb7e2139ceb23828e61c441b7e9858501c0fb6fd85e881b4034882627b614","last_reissued_at":"2026-05-18T03:14:17.381098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:17.381098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the twisted Alexander polynomial for representations into SL_2(C)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anh T. Tran","submitted_at":"2013-02-07T02:39:39Z","abstract_excerpt":"We study the twisted Alexander polynomial $\\Delta_{K,\\rho}$ of a knot $K$ associated to a non-abelian representation $\\rho$ of the knot group into $SL_2(\\BC)$. It is known for every knot $K$ that if $K$ is fibered, then for every non-abelian representation, $\\Delta_{K,\\rho}$ is monic and has degree $4g(K)-2$ where $g(K)$ is the genus of $K$. Kim and Morifuji recently proved the converse for 2-bridge knots. 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