{"paper":{"title":"Semifree Hamiltonian circle actions on 6-dimensional symplectic manifolds with non-isolated fixed point set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dong Youp Suh, Taekgyu Hwang, Yunhyung Cho","submitted_at":"2010-05-03T06:21:36Z","abstract_excerpt":"Let $(M, \\omega)$ be a 6-dimensional closed symplectic manifold with a symplectic $S^1$-action with $M^{S^1} \\neq \\emptyset$ and $\\dim M^{S^1} \\leq 2$. Assume that $\\omega$ is integral with a generalized moment map $\\mu$. We first prove that the action is Hamiltonian if and only if $b_2^+(M_{\\red})=1$, where $M_{\\red}$ is any reduced space with respect to $\\mu$. It means that if the action is non-Hamiltonian, then $b_2^+(M_{\\red}) \\geq 2$. Secondly, we focus on the case when the action is semifree and Hamiltonian. We prove that if $M^{S^1}$ consists of surfaces, then the number $k$ of fixed su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0193","kind":"arxiv","version":5},"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"}