{"paper":{"title":"Hamiltonian circle actions with minimal fixed sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Hui Li, Susan Tolman","submitted_at":"2009-05-25T18:23:57Z","abstract_excerpt":"Consider an effective Hamiltonian circle action on a compact symplectic $2n$-dimensional manifold $(M, \\omega)$. Assume that the fixed set $M^{S^1}$ is {\\em minimal}, in two senses: it has exactly two components, $X$ and $Y$, and $\\dim(X) + \\dim(Y) = \\dim(M) - 2$.\n  We prove that the integral cohomology ring and Chern classes of $M$ are isomorphic to either those of $\\CP^n$ or (if $n \\neq 1$ is odd) to those of $\\Gt_2(\\R^{n+2})$, the Grassmannian of oriented two-planes in $\\R^{n+2}$. In particular, $H^i(M;\\Z) = H^i(\\CP^n;\\Z)$ for all $i$, and the Chern classes of $M$ are determined by the inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4049","kind":"arxiv","version":3},"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"}