{"paper":{"title":"The diffeomorphism type of canonical integrations of Poisson tensors on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David Mart\\'inez Torres","submitted_at":"2014-08-20T15:06:57Z","abstract_excerpt":"A surface $\\Sigma$ endowed with a Poisson tensor $\\pi$ is known to admit a canonical integration $\\mathcal{G}(\\pi)$, which is a 4-dimensional manifold with a (symplectic) groupoid structure. In this short note we show that when $\\pi$ is not an area form on the 2-sphere, then $\\mathcal{G}(\\pi)$ is diffeomorphic to the cotangent bundle $T^*\\Sigma$, this extending results in \\cite{Ma09} and \\cite{BCST12}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4689","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"}