{"paper":{"title":"Darboux chart on Projective limit of weak symplectic Banach manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.SG","authors_text":"Pradip Kumar","submitted_at":"2013-09-06T16:29:38Z","abstract_excerpt":"Suppose M be the projective limit of weak symplectic Banach manifolds \\{(M_i,\\phi_{ij})\\}_{i,j\\in\\mathbb N}, where M_i are modeled over reflexive Banach space and \\sigma is compatible with the inverse system(defined in the article). We associate to each point x\\in M, a Fr\\'{e}chet space H_x(defined in section 3). We prove that if H_x are locally constant, then with certain smoothness and boundedness condition, there exists Darboux chart for the weak symplectic structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1693","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":""},"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"}