{"paper":{"title":"Hamiltonian circle actions on eight dimensional manifolds with minimal fixed sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Donghoon Jang, Susan Tolman","submitted_at":"2014-08-27T22:16:47Z","abstract_excerpt":"Consider a Hamiltonian circle action on a closed $8$-dimensional symplectic manifold $M$ with exactly five fixed points, which is the smallest possible fixed set. In their paper, L. Godinho and S. Sabatini show that if $M$ satisfies an extra \"positivity condition\" then the isotropy weights at the fixed points of $M$ agree with those of some linear action on $\\mathbb{CP}^4$. Therefore, the (equivariant) cohomology rings and the (equivariant) Chern classes of $M$ and $\\mathbb{CP}^4$ agree; in particular, $H^*(M;\\mathbb{Z}) \\simeq \\mathbb{Z}[y]/y^5$ and $c(TM) = (1+y)^5$. In this paper, we prove "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6580","kind":"arxiv","version":2},"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"}