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We do this by explicitly computing the spectrum of the Dirac operator for $SU(2)/\\Gamma$ equipped with the trivial spin structure and a selection of metrics. Here $\\Gamma$ is a finite subgroup of SU(2). In the case where $\\Gamma$ is cyclic, or dicyclic, we consider the one-parameter family of Berger metrics, which includes the round metric, and when $\\Gamma$ "},"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":"1010.1827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-09T10:18:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2acff1efaacb78593b7f5c15adc76401cd7970d78583094dc48e7df2bc8a663e","abstract_canon_sha256":"f37c1c6271eb23c771754c56db968315a4c87491db23b2e4497b33c6f704e552"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:51.127892Z","signature_b64":"roh3uqHajt8kSBLHY2tcijG4wBRjufDj8BuXd6b8fSHRIf7lzd84wzyuxt0Ayv0K+iw4yxOCYUP7PVSaSY57Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"261cbc7038ce5bad4a88afc65beef2a5fdb1c62e0e1ea07f34ae74d660f0804d","last_reissued_at":"2026-05-18T04:20:51.127307Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:51.127307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonperturbative Spectral Action of Round Coset Spaces of SU(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Kevin Teh","submitted_at":"2010-10-09T10:18:59Z","abstract_excerpt":"We compute the spectral action of $SU(2)/\\Gamma$ with the trivial spin structure and the round metric and find it in each case to be equal to $\\frac{1}{|\\Gamma|} (\\Lambda^3 \\hat{f}^{(2)}(0) - 1/4\\Lambda \\hat{f}(0))+ O(\\Lambda^{-\\infty})$. We do this by explicitly computing the spectrum of the Dirac operator for $SU(2)/\\Gamma$ equipped with the trivial spin structure and a selection of metrics. Here $\\Gamma$ is a finite subgroup of SU(2). 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