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For the proof, they constructed a homomorphism from the space of quasi-morphisms on the braid group to the space of quasi-morphisms on ${\\rm Diff}_\\Omega^\\infty (D^2, \\partial D^2)$. In this paper, we study this homomorphism and prove its injectivity. We give several applications of our result to stable commutator length of some element of ${\\rm Diff}_\\Omega^\\infty (D^2, \\partial D^2)$ and conjugation-invariant norms on ${\\rm Diff}_\\Omega^\\infty (D^2, \\partial D^2)$.", "subitem_description_type": "Abstract"}]}, "item_7_full_name_3": {"attribute_name": "\u8457\u8005\u5225\u540d", "attribute_value_mlt": [{"nameIdentifiers": [{"nameIdentifier": "11753", "nameIdentifierScheme": "WEKO"}], "names": [{"name": "\u77f3\u7530, \u667a\u5f66"}]}]}, "item_7_identifier_registration": {"attribute_name": "ID\u767b\u9332", "attribute_value_mlt": [{"subitem_identifier_reg_text": "10.15083/00005642", "subitem_identifier_reg_type": "JaLC"}]}, "item_7_select_21": {"attribute_name": "\u5b66\u4f4d", "attribute_value_mlt": [{"subitem_select_item": "doctoral"}]}, "item_7_text_22": {"attribute_name": "\u5b66\u4f4d\u5206\u91ce", "attribute_value_mlt": [{"subitem_text_value": "Mathematical Sciences (\u6570\u7406\u79d1\u5b66)"}]}, "item_7_text_24": {"attribute_name": "\u7814\u7a76\u79d1\u30fb\u5c02\u653b", "attribute_value_mlt": [{"subitem_text_value": "Graduate School of Mathematical Sciences (\u6570\u7406\u79d1\u5b66\u7814\u7a76\u79d1)"}]}, "item_7_text_36": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"subitem_text_value": "Thesis"}]}, "item_7_text_4": {"attribute_name": "\u8457\u8005\u6240\u5c5e", "attribute_value_mlt": [{"subitem_text_value": "\u6771\u4eac\u5927\u5b66\u5927\u5b66\u9662\u6570\u7406\u79d1\u5b66\u7814\u7a76\u79d1"}, {"subitem_text_value": "Graduate School of Mathematical Sciences, The University of Tokyo"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Ishida, Tomohiko"}], "nameIdentifiers": [{"nameIdentifier": "11752", "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": "2017-06-01"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "IshidaT_25_3_PhD_a.pdf", "filesize": [{"value": "1.4 MB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 1400000.0, "url": {"label": "IshidaT_25_3_PhD_a.pdf", "url": "https://repository.dl.itc.u-tokyo.ac.jp/record/5651/files/IshidaT_25_3_PhD_a.pdf"}, "version_id": "ebcef54a-263d-4f3e-97d5-64b8419e64e6"}, {"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2017-06-01"}], "displaytype": "detail", "download_preview_message": "", "file_order": 1, "filename": "IshidaT_25_3_PhD_b.pdf", "filesize": [{"value": "159.8 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 159800.0, "url": {"label": "IshidaT_25_3_PhD_b.pdf", "url": "https://repository.dl.itc.u-tokyo.ac.jp/record/5651/files/IshidaT_25_3_PhD_b.pdf"}, "version_id": "abb1fddf-90c6-481a-b686-9252065a6171"}]}, "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": "thesis", "resourceuri": "http://purl.org/coar/resource_type/c_46ec"}]}, "item_title": "Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk"}]}, "item_type_id": "7", "owner": "1", "path": ["312/391", "9/233/280"], "permalink_uri": "https://doi.org/10.15083/00005642", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_name_i18n": "\u516c\u958b\u65e5", "attribute_value": "2014-07-15"}, "publish_date": "2014-07-15", "publish_status": "0", "recid": "5651", "relation": {}, "relation_version_is_last": true, "title": ["Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk"], "weko_shared_id": 2}