WEKO3
アイテム
{"_buckets": {"deposit": "6165a130-245f-4472-b17b-065a1a38013f"}, "_deposit": {"id": "40044", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "40044"}, "status": "published"}, "_oai": {"id": "oai:repository.dl.itc.u-tokyo.ac.jp:00040044", "sets": ["6915", "6916"]}, "item_4_biblio_info_7": {"attribute_name": "書誌情報", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2011-12-09", "bibliographicIssueDateType": "Issued"}, "bibliographicIssueNumber": "2", "bibliographicPageEnd": "268", "bibliographicPageStart": "239", "bibliographicVolumeNumber": "18", "bibliographic_titles": [{"bibliographic_title": "Journal of mathematical sciences, the University of Tokyo"}]}]}, "item_4_description_5": {"attribute_name": "抄録", "attribute_value_mlt": [{"subitem_description": "It is a natural consequence of fundamental properties of the Casson invariant that the Rokhlin invariant μ(M) of an amphichiral integral homology 3-sphere M vanishes. In this paper, we give a new direct proof of this vanishing property. For such an M, we construct a manifold pair (Y, Q) of dimensions 6 and 3 equipped with some additional structure (6-dimensional spin e-manifold), such that Q ≅ M ∐ M ∐ (-M), and (Y, Q) ≅ (-Y, -Q). We prove that (Y, Q) bounds a 7-dimensional spin e-manifold (Z, X) by studying the cobordism group of 6-dimensional spin e-manifolds and the Z/2-action on the two-point configuration space of M \\ {pt}. For any such (Z, X), the signature of X vanishes, and this implies μ(M) = 0. The idea of the construction of (Y, Q) comes from the definition of the Kontsevich-Kuperberg-Thurston invariant for rational homology 3-spheres.", "subitem_description_type": "Abstract"}]}, "item_4_publisher_20": {"attribute_name": "出版者", "attribute_value_mlt": [{"subitem_publisher": "Graduate School of Mathematical Sciences, The University of Tokyo"}]}, "item_4_source_id_10": {"attribute_name": "書誌レコードID", "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": "日本十進分類法", "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": "57M27(MSC2010)"}, {"subitem_text_value": "57N70(MSC2010)"}, {"subitem_text_value": "57R20(MSC2010)"}, {"subitem_text_value": "55R80(MSC2010)"}]}, "item_4_text_33": {"attribute_name": "原稿受領日", "attribute_value_mlt": [{"subitem_text_value": "2011-05-19"}]}, "item_4_text_34": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"subitem_text_value": "Departmental Bulletin Paper"}]}, "item_4_text_4": {"attribute_name": "著者所属", "attribute_value_mlt": [{"subitem_text_value": "Shibano Patent Office"}]}, "item_creator": {"attribute_name": "著者", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Moriyama, Tetsuhiro"}], "nameIdentifiers": [{"nameIdentifier": "92493", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "ファイル情報", "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": "jms180205.pdf", "filesize": [{"value": "232.5 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 232500.0, "url": {"label": "jms180205.pdf", "url": "https://repository.dl.itc.u-tokyo.ac.jp/record/40044/files/jms180205.pdf"}, "version_id": "d6bafc51-3460-40a6-8cb1-3ad06e4d654d"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "On the Vanishing of the Rokhlin Invariant", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "On the Vanishing of the Rokhlin Invariant"}]}, "item_type_id": "4", "owner": "1", "path": ["6915", "6916"], "permalink_uri": "http://hdl.handle.net/2261/52707", "pubdate": {"attribute_name": "公開日", "attribute_value": "2012-12-12"}, "publish_date": "2012-12-12", "publish_status": "0", "recid": "40044", "relation": {}, "relation_version_is_last": true, "title": ["On the Vanishing of the Rokhlin Invariant"], "weko_shared_id": null}
On the Vanishing of the Rokhlin Invariant
http://hdl.handle.net/2261/52707
http://hdl.handle.net/2261/52707cf207227-275a-4f29-a36f-87e9270529d3
名前 / ファイル | ライセンス | アクション |
---|---|---|
jms180205.pdf (232.5 kB)
|
|
Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
---|---|---|---|---|---|---|
公開日 | 2012-12-12 | |||||
タイトル | ||||||
タイトル | On the Vanishing of the Rokhlin Invariant | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Moriyama, Tetsuhiro
× Moriyama, Tetsuhiro |
|||||
著者所属 | ||||||
著者所属 | Shibano Patent Office | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | It is a natural consequence of fundamental properties of the Casson invariant that the Rokhlin invariant μ(M) of an amphichiral integral homology 3-sphere M vanishes. In this paper, we give a new direct proof of this vanishing property. For such an M, we construct a manifold pair (Y, Q) of dimensions 6 and 3 equipped with some additional structure (6-dimensional spin e-manifold), such that Q ≅ M ∐ M ∐ (-M), and (Y, Q) ≅ (-Y, -Q). We prove that (Y, Q) bounds a 7-dimensional spin e-manifold (Z, X) by studying the cobordism group of 6-dimensional spin e-manifolds and the Z/2-action on the two-point configuration space of M \ {pt}. For any such (Z, X), the signature of X vanishes, and this implies μ(M) = 0. The idea of the construction of (Y, Q) comes from the definition of the Kontsevich-Kuperberg-Thurston invariant for rational homology 3-spheres. | |||||
書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 18, 号 2, p. 239-268, 発行日 2011-12-09 |
|||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 13405705 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA11021653 | |||||
日本十進分類法 | ||||||
主題 | 415 | |||||
主題Scheme | NDC | |||||
Mathematical Reviews Number | ||||||
MR | ||||||
Mathmatical Subject Classification | ||||||
57M27(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
57N70(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
57R20(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
55R80(MSC2010) | ||||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
2011-05-19 |