{"paper":{"title":"Extending compact Hamiltonian $\\mathbb{S}^1$-spaces to integrable systems with mild degeneracies in dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Joseph Palmer, Sonja Hohloch","submitted_at":"2021-05-02T18:09:27Z","abstract_excerpt":"Given any compact connected four dimensional symplectic manifold $(M,\\omega)$ and smooth function $J\\colon M\\to \\mathbb{R}$ which generates an effective $\\mathbb{S}^1$-action, we show that there exists a smooth function $H\\colon M\\to\\mathbb{R}$ such that $(M,\\omega,(J,H))$ is a completely (Liouville) integrable system of a type we call hypersemitoric -- these are systems for which all singularities are non-degenerate, except possibly for a finite number of families of degenerate points of a relatively tame type called parabolic (also sometimes called cuspidal). Such an $(M,\\omega,J)$ is often "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.00523","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.00523/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}