{"created":"2022-01-27T08:05:28.183155+00:00","id":2004448,"links":{},"metadata":{"_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","1642838403551:1642838406414"]},"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^<2n+1>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^<2n+1>である.\\n(ii)P^l_<k,n>で,多項式 f(z)=z^k+a_1z^<k-1>+【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_<k,n>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_<k,n>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^<n-1>)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^<2n+1>. 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^<2n+1>.\\n(ii)Let P_<k,n> 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_<k,n>, but most part was left unknown. The second achievement of research is to determine the stable homotopy type of P^l_<k,n> completely, and to show that the homology groups of P^l_<k,n> are determined from this. As a result, I solved Arnold's 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","filename":"15540087-2.pdf","mimetype":"application/pdf","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","filename":"15540087-1.pdf","mimetype":"application/pdf","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"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2009-03-17"},"publish_date":"2009-03-17","publish_status":"0","recid":"2004448","relation_version_is_last":true,"title":["対合同変正則写像空間の位相幾何"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-10-31T01:57:53.172693+00:00"}