{"paper":{"title":"Symplectic forms on the space of embedded symplectic surfaces and their reductions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Liat Kessler","submitted_at":"2011-08-02T18:34:42Z","abstract_excerpt":"Let (M,\\omega) be a symplectic manifold, and (\\Sigma,\\sigma) a closed connected symplectic 2-manifold. We construct a weakly symplectic form {\\omega^{D}}_{(\\Sigma, \\sigma)} on the space of immersions \\Sigma \\to M that is a special case of Donaldson's form. We show that the restriction of {\\omega^{D}}_{(\\Sigma,\\sigma)} to any orbit of the group of Hamiltonian symplectomorphisms through a symplectic embedding (\\Sigma,\\sigma) \\to (M,\\omega) descends to a weakly symplectic form \\omega^D_{\\red} on the quotient by Sympl(\\Sigma,\\sigma), and that the obtained symplectic space is a symplectic quotient "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0636","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"}