{"paper":{"title":"Nontrivial bundles of coadjoint orbits over $S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David Mart\\'inez Torres, Ignasi Mundet i Riera","submitted_at":"2017-09-15T15:00:05Z","abstract_excerpt":"Let $G$ be a compact connected semisimple Lie group with Lie algebra $\\mathfrak{g}$. Let $\\mathcal{O}\\subset\\mathfrak{g}^*$ be a coadjoint orbit. The action of $G$ on $\\mathcal{O}$ induces a morphism $\\rho:G\\to \\mathrm{Homeo}(\\mathcal{O})$. We prove that the induced map $\\pi_1(\\rho):\\pi_1(G)\\to\\pi_1(\\mathrm{Homeo}(\\mathcal{O}))$ is injective. This strengthens a theorem of McDuff and Tolman (conjectured by Weinstein in 1989) according to which the analogous map $G\\to\\mathrm{Ham}(\\mathcal{O})$ is injective on fundamental groups, where $\\mathrm{Ham}(\\mathcal{O})$ is the group of Hamiltonian diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05247","kind":"arxiv","version":1},"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"}