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Fixed-point homogeneous manifolds with positive sectional curvature have been completely classified. We classify fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected 4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure."},"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":"0911.1254","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-06T13:58:18Z","cross_cats_sorted":[],"title_canon_sha256":"39bb2bff30bd91e68ece3791ff1f25f607fe0041816982d14ec9b6ebe058a1b1","abstract_canon_sha256":"476c74c9399ba444c5d5018a06a19e8f41f9c1a427993cf0197fb20057744074"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:14.783190Z","signature_b64":"LuI9mvQncL8L+zHkMDG/mpbbuWKwb4OvsFuOkL712MwDOQp6Ht7f7pzDf4uAYN795gt8TvkC5BNBlkOjrwQgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf304eadbf95e1ac8e5b36e3a157be554a0224495761cf75ce4d3cf6ecfc7679","last_reissued_at":"2026-05-18T04:20:14.782745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:14.782745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonnegatively curved fixed point homogeneous manifolds in low dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Fernando Galaz-Garcia","submitted_at":"2009-11-06T13:58:18Z","abstract_excerpt":"Let $G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $M$ with nonempty fixed point set $M^G$. 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