{"paper":{"title":"Complex cobordism, Hamiltonian loops and global Kuranishi charts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.SG","authors_text":"Ivan Smith, Mark McLean, Mohammed Abouzaid","submitted_at":"2021-10-27T09:59:17Z","abstract_excerpt":"Let $(X,\\omega)$ be a closed symplectic manifold. A loop $\\phi: S^1 \\to \\mathrm{Diff}(X)$ of diffeomorphisms of $X$ defines a fibration $\\pi: P_{\\phi} \\to S^2$. By applying Gromov-Witten theory to moduli spaces of holomorphic sections of $\\pi$, Lalonde, McDuff and Polterovich proved that if $\\phi$ lifts to the Hamiltonian group $\\mathrm{Ham}(X,\\omega)$, then the rational cohomology of $P_{\\phi}$ splits additively. We prove, with the same assumptions, that the $\\mathbb{E}$-generalised cohomology of $P_{\\phi}$ splits additively for any complex-oriented cohomology theory $\\mathbb{E}$, in particul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14320","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.14320/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"}