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In particular when a structure of a singular Lagrangian fibration is given on a closed symplectic manifold, its Riemann-Roch number is described as the sum of the number of nonsingular Bohr-Sommerfeld fibers and a contribution of the singular fibers. A key step of the proof is formally explained as a version of Witten\u0027s deformation applied to a Hilbert bundle.", "subitem_description_type": "Abstract"}]}, "item_4_publisher_20": {"attribute_name": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "Graduate School of Mathematical Sciences, The University of Tokyo"}]}, "item_4_source_id_10": {"attribute_name": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "attribute_value_mlt": [{"subitem_source_identifier": "AA11021653", "subitem_source_identifier_type": "NCID"}]}, "item_4_source_id_8": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "13405705", "subitem_source_identifier_type": "ISSN"}]}, "item_4_subject_15": {"attribute_name": "\u65e5\u672c\u5341\u9032\u5206\u985e\u6cd5", "attribute_value_mlt": [{"subitem_subject": "415", "subitem_subject_scheme": "NDC"}]}, "item_4_text_16": {"attribute_name": "Mathematical Reviews Number", "attribute_value_mlt": [{"subitem_text_value": "MR"}]}, "item_4_text_17": {"attribute_name": "Mathmatical Subject Classification", "attribute_value_mlt": [{"subitem_text_value": "53D50(MSC2000)"}, {"subitem_text_value": "58J20(MSC2000)"}]}, "item_4_text_33": {"attribute_name": "\u539f\u7a3f\u53d7\u9818\u65e5", "attribute_value_mlt": [{"subitem_text_value": "2008-04-18"}]}, "item_4_text_34": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"subitem_text_value": "Departmental Bulletin Paper"}]}, "item_4_text_4": {"attribute_name": "\u8457\u8005\u6240\u5c5e", "attribute_value_mlt": [{"subitem_text_value": "Department of Mathematics, Gakushuin University"}, {"subitem_text_value": "Graduate School of Mathematical Sciences, The University of Tokyo"}, {"subitem_text_value": "Department of Mathematics, Graduate School of Science and Technology, Meiji University"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Fujita, Hajime"}], "nameIdentifiers": [{"nameIdentifier": "92519", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "Furuta, Mikio"}], "nameIdentifiers": [{"nameIdentifier": "92520", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "Yoshida, Takahiko"}], "nameIdentifiers": [{"nameIdentifier": "92521", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2017-06-14"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "jms170101.pdf", "filesize": [{"value": "207.2 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 207200.0, "url": {"label": "jms170101.pdf", "url": "https://repository.dl.itc.u-tokyo.ac.jp/record/40063/files/jms170101.pdf"}, "version_id": "71fe6b1f-846e-45a7-973e-22904f178d01"}]}, "item_keyword": {"attribute_name": "\u30ad\u30fc\u30ef\u30fc\u30c9", "attribute_value_mlt": [{"subitem_subject": "Geometric quantization", "subitem_subject_scheme": "Other"}, {"subitem_subject": "index theory", "subitem_subject_scheme": "Other"}, {"subitem_subject": "localization", "subitem_subject_scheme": "Other"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Torus Fibrations and Localization of Index I : Polarization and Acyclic Fibrations", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Torus Fibrations and Localization of Index I : Polarization and Acyclic Fibrations"}]}, "item_type_id": "4", "owner": "1", "path": ["312/6865/6919/6927", "9/504/6868/6921/6928"], "permalink_uri": "http://hdl.handle.net/2261/52392", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_value": "2012-10-22"}, "publish_date": "2012-10-22", "publish_status": "0", "recid": "40063", "relation": {}, "relation_version_is_last": true, "title": ["Torus Fibrations and Localization of Index I : Polarization and Acyclic Fibrations"], "weko_shared_id": null}