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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.0636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-08-02T18:34:42Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b3884eb97e0861f3b9c24f469101a7ab3b7dbae03eca7a926958ac26336019ec","abstract_canon_sha256":"623d4a4e6789297b4ce806e2ead01110cc9de20ec0ed406459127d20e82b7eab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:23.762013Z","signature_b64":"SkEB3nxR5O6vPuLWOtRQW48XUwzjdVMG77AQbR26mtgjDm6IVMx+30VT/SdZ/2vgA9nQ2cbcW5kXsSXtjcCrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"886521ca13b5e51a1a9322648a5b860f3726ae92f350403f8746e46e04de3dc5","last_reissued_at":"2026-05-18T04:16:23.761396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:23.761396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1108.0636","created_at":"2026-05-18T04:16:23.761494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.0636v1","created_at":"2026-05-18T04:16:23.761494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0636","created_at":"2026-05-18T04:16:23.761494+00:00"},{"alias_kind":"pith_short_12","alias_value":"RBSSDSQTWXSR","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RBSSDSQTWXSRUGUT","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RBSSDSQT","created_at":"2026-05-18T12:26:41.206345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RBSSDSQTWXSRUGUTEJSIUW4GB4","json":"https://pith.science/pith/RBSSDSQTWXSRUGUTEJSIUW4GB4.json","graph_json":"https://pith.science/api/pith-number/RBSSDSQTWXSRUGUTEJSIUW4GB4/graph.json","events_json":"https://pith.science/api/pith-number/RBSSDSQTWXSRUGUTEJSIUW4GB4/events.json","paper":"https://pith.science/paper/RBSSDSQT"},"agent_actions":{"view_html":"https://pith.science/pith/RBSSDSQTWXSRUGUTEJSIUW4GB4","download_json":"https://pith.science/pith/RBSSDSQTWXSRUGUTEJSIUW4GB4.json","view_paper":"https://pith.science/paper/RBSSDSQT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.0636&json=true","fetch_graph":"https://pith.science/api/pith-number/RBSSDSQTWXSRUGUTEJSIUW4GB4/graph.json","fetch_events":"https://pith.science/api/pith-number/RBSSDSQTWXSRUGUTEJSIUW4GB4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RBSSDSQTWXSRUGUTEJSIUW4GB4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RBSSDSQTWXSRUGUTEJSIUW4GB4/action/storage_attestation","attest_author":"https://pith.science/pith/RBSSDSQTWXSRUGUTEJSIUW4GB4/action/author_attestation","sign_citation":"https://pith.science/pith/RBSSDSQTWXSRUGUTEJSIUW4GB4/action/citation_signature","submit_replication":"https://pith.science/pith/RBSSDSQTWXSRUGUTEJSIUW4GB4/action/replication_record"}},"created_at":"2026-05-18T04:16:23.761494+00:00","updated_at":"2026-05-18T04:16:23.761494+00:00"}