{"_buckets": {"deposit": "c19b4fa3-eb40-4a7d-b5ce-747921fea44b"}, "_deposit": {"id": "2004448", "owners": [1], "pid": {"revision_id": 0, "type": "depid", "value": "2004448"}, "status": "published"}, "_oai": {"id": "oai:u-ryukyu.repo.nii.ac.jp:02004448", "sets": ["1642838403123", "1642838406414"]}, "author_link": [], "item_1617186331708": {"attribute_name": "Title", "attribute_value_mlt": [{"subitem_1551255647225": "対合同変正則写像空間の位相幾何", "subitem_1551255648112": "ja"}, {"subitem_1551255647225": "Topology of spaces of conjugation-equivariant holomorphic maps", "subitem_1551255648112": "en"}]}, "item_1617186419668": {"attribute_name": "Creator", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "神山, 靖彦", "creatorNameLang": "ja"}]}, {"creatorNames": [{"creatorName": "志賀, 博雄", "creatorNameLang": "ja"}]}, {"creatorNames": [{"creatorName": "手塚, 康誠", "creatorNameLang": "ja"}]}, {"creatorNames": [{"creatorName": "Kamiyama, Yasuhiko", "creatorNameLang": "en"}]}, {"creatorNames": [{"creatorName": "Shiga, Hiroo", "creatorNameLang": "en"}]}, {"creatorNames": [{"creatorName": "Tezuka, Michishige", "creatorNameLang": "en"}]}]}, "item_1617186476635": {"attribute_name": "Access Rights", "attribute_value_mlt": [{"subitem_1522299639480": "open access", "subitem_1600958577026": "http://purl.org/coar/access_right/c_abf2"}]}, "item_1617186609386": {"attribute_name": "Subject", "attribute_value_mlt": [{"subitem_1522299896455": "ja", "subitem_1522300014469": "Other", "subitem_1523261968819": "有理関数"}, {"subitem_1522299896455": "ja", "subitem_1522300014469": "Other", "subitem_1523261968819": "複素共役対合"}, {"subitem_1522299896455": "ja", "subitem_1522300014469": "Other", "subitem_1523261968819": "多項式"}, {"subitem_1522299896455": "ja", "subitem_1522300014469": "Other", "subitem_1523261968819": "重根"}, {"subitem_1522299896455": "ja", "subitem_1522300014469": "Other", "subitem_1523261968819": "配置空間"}, {"subitem_1522299896455": "ja", "subitem_1522300014469": "Other", "subitem_1523261968819": "ループ空間"}, {"subitem_1522299896455": "ja", "subitem_1522300014469": "Other", "subitem_1523261968819": "安定分解"}, {"subitem_1522299896455": "ja", "subitem_1522300014469": "Other", "subitem_1523261968819": "生成多様体"}, {"subitem_1522299896455": "en", "subitem_1522300014469": "Other", "subitem_1523261968819": "rational function"}, {"subitem_1522299896455": "en", "subitem_1522300014469": "Other", "subitem_1523261968819": "conjugation"}, {"subitem_1522299896455": "en", "subitem_1522300014469": "Other", "subitem_1523261968819": "polynomial"}, {"subitem_1522299896455": "en", "subitem_1522300014469": "Other", "subitem_1523261968819": "multiple root"}, {"subitem_1522299896455": "en", "subitem_1522300014469": "Other", "subitem_1523261968819": "configuration space"}, {"subitem_1522299896455": "en", "subitem_1522300014469": "Other", "subitem_1523261968819": "loop space"}, {"subitem_1522299896455": "en", "subitem_1522300014469": "Other", "subitem_1523261968819": "stable splitting"}, {"subitem_1522299896455": "en", "subitem_1522300014469": "Other", "subitem_1523261968819": "generating variety"}]}, "item_1617186626617": {"attribute_name": "Description", "attribute_value_mlt": [{"subitem_description": "科研費番号: 15540087", "subitem_description_type": "Other"}, {"subitem_description": "平成15年度~平成17年度科学研究費補助金(基盤研究(C))成果報告書", "subitem_description_type": "Other"}, {"subitem_description": "(研究概要)Rat_k(CP^n)でS^2からCP^nへの基点を保つ正則写像空間を表す.Rat_k(CP^n)の安定ホモトピー型は,対応する連続写像空間 Ω^2S^\u003c2n+1\u003eのSnaith stable summandsで記述できるという定理は,報告者及びCohen-Cohen-Mann-Milgramにより証明されていた.本研究の目的は,この定理を次の2方面で一般化することである.\\n(i)Rat_k(CP^n)の上には,複素共役による対合が作用する.この対合と可換な正則写像全体を RRat_k(CP^n)で表す.このRRat_k(CP^n)のホモトピー型は,n=1のときにはBrockett及びSegalにより決定されていた.しかし,n【greater than or equal】2にときには未解決であった.本研究の第一の成果はRRat_k(CP^n)の安定ホモトピー型を完全に決定したことである.この際,対応する対合同変連続空間は,ΩS^n×Ω^2S^\u003c2n+1\u003eである.\\n(ii)P^l_\u003ck,n\u003eで,多項式 f(z)=z^k+a_1z^\u003ck-1\u003e+【triple pond】+a_kで,n重根が高々l個であるものの空間を表す.Arnoldは,1970年にP^l_\u003ck,n\u003eのホモロジーを数学的帰納法により決定しようとしたが,未解決な部分が多かった.本研究の第二の成果は,P^l_\u003ck,n\u003eの安定ホモトピー型を完全に決定し,そこからホモロジーも読み取れることを示したことである.従って,Arnoldの問題は完全に解決されたことになる.この際,使用するstable summandsは,Rat_k(CP^\u003cn-1\u003e)のある一般化のstable summandsである.この一般化は,k次多項式のn組で,共通根が高々l個というもののなす空間である.つまり,単独の多項式のなす空間と,多項式の n組のなす空間との間の関係を解明したわけである.\\nなお,(ii)の研究実績は高く評価されている.一例として,研究代表者は,2005年7月に東大で開催されたCOE国際会議で主要講演を行った.", "subitem_description_type": "Other"}, {"subitem_description": "Let Rat_k(CP^n) be the space of basepoint-preserving holomorphic maps fromS^2 to CP^n. This is a subspace of Ω^2_kCP^n. A theorem by me and Cohen-Cohen-Mann-Milgram tells that the stable homotopy type of Rat_k(CP^n) is described in terms of stable summands of Ω^2S^\u003c2n+1\u003e. The purpose of this research is to generalize the theorem in two directions.\\n(i)Let RRat_k(CP^n) be the subspace of Rat_k(CP^n) of maps which commute with an involution by complex conjugation. Brockett and Segal determined the homotopy type of RRat_k(CP^1). But the case n【greater than or equal】2 was unknown. The first achievement of this research is to determine the stable homotopy type of RRat_k(CP^n) completely. In this case, the corresponding continuous mapping space is ΩS^n×Ω^2S^\u003c2n+1\u003e.\\n(ii)Let P_\u003ck,n\u003e be the space of polynomials such that the number of n-fold roots is at most l. In 1970, Arnold tried to determine the homology group of P^l_\u003ck,n\u003e, but most part was left unknown. The second achievement of research is to determine the stable homotopy type of P^l_\u003ck,n\u003e completely, and to show that the homology groups of P^l_\u003ck,n\u003e are determined from this. As a result, I solved Arnold\u0027s problem completely. Roughly, the main result is to prove a relationship between a space of single polynomials and a space of n-tuples of polynomials.\\nThe achievement in (ii) was highly evaluated. For example, I gave a plenary talk at the COE International Conference held at the University of Tokyo in July 2005.", "subitem_description_type": "Other"}, {"subitem_description": "(p.154-)Configuration spaces and rational functions / Yasuhiko Kamiyama", "subitem_description_type": "Other"}, {"subitem_description": "未公開:P.15~154(論文別刷のため)", "subitem_description_type": "Other"}, {"subitem_description": "研究報告書", "subitem_description_type": "Other"}]}, "item_1617186643794": {"attribute_name": "Publisher", "attribute_value_mlt": [{"subitem_1522300295150": "ja", "subitem_1522300316516": "神山靖彦"}]}, "item_1617186702042": {"attribute_name": "Language", "attribute_value_mlt": [{"subitem_1551255818386": "jpn"}]}, "item_1617186783814": {"attribute_name": "Identifier", "attribute_value_mlt": [{"subitem_identifier_type": "HDL", "subitem_identifier_uri": "http://hdl.handle.net/20.500.12000/9229"}]}, "item_1617186920753": {"attribute_name": "Source Identifier", "attribute_value_mlt": [{"subitem_1522646500366": "NCID", "subitem_1522646572813": "BA79181376"}]}, "item_1617187056579": {"attribute_name": "Bibliographic Information", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2006-03", "bibliographicIssueDateType": "Issued"}, "bibliographicPageStart": "none"}]}, "item_1617258105262": {"attribute_name": "Resource Type", "attribute_value_mlt": [{"resourcetype": "research report", "resourceuri": "http://purl.org/coar/resource_type/c_18ws"}]}, "item_1617265215918": {"attribute_name": "Version Type", "attribute_value_mlt": [{"subitem_1522305645492": "VoR", "subitem_1600292170262": "http://purl.org/coar/version/c_970fb48d4fbd8a85"}]}, "item_1617605131499": {"attribute_name": "File", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_access", "download_preview_message": "", "file_order": 0, "filename": "15540087-2.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2004448/files/15540087-2.pdf"}, "version_id": "c2f72a3d-1e8b-4d50-ae5b-63b802d9de20"}, {"accessrole": "open_access", "download_preview_message": "", "file_order": 1, "filename": "15540087-1.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2004448/files/15540087-1.pdf"}, "version_id": "c6808121-71cd-4442-83f1-b0a5c74356e6"}]}, "item_title": "対合同変正則写像空間の位相幾何", "item_type_id": "15", "owner": "1", "path": ["1642838403123", "1642838406414"], "permalink_uri": "http://hdl.handle.net/20.500.12000/9229", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2009-03-17"}, "publish_date": "2009-03-17", "publish_status": "0", "recid": "2004448", "relation": {}, "relation_version_is_last": true, "title": ["対合同変正則写像空間の位相幾何"], "weko_shared_id": -1}
http://hdl.handle.net/20.500.12000/9229
http://hdl.handle.net/20.500.12000/9229