{"created":"2022-01-27T08:05:31.216529+00:00","id":2004450,"links":{},"metadata":{"_buckets":{"deposit":"eb7d9961-a4fc-4a62-a5be-80f0bc69729f"},"_deposit":{"id":"2004450","owners":[1],"pid":{"revision_id":0,"type":"depid","value":"2004450"},"status":"published"},"_oai":{"id":"oai:u-ryukyu.repo.nii.ac.jp:02004450","sets":["1642838403123","1642838403551:1642838406414"]},"author_link":[],"item_1617186331708":{"attribute_name":"Title","attribute_value_mlt":[{"subitem_1551255647225":"有理関数空間の完備化の位相幾何","subitem_1551255648112":"ja"},{"subitem_1551255647225":"Topology of completions of the space of rational functions","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":"完備化"},{"subitem_1522299896455":"ja","subitem_1522300014469":"Other","subitem_1523261968819":"ハープ空間"},{"subitem_1522299896455":"ja","subitem_1522300014469":"Other","subitem_1523261968819":"ホモロジー"},{"subitem_1522299896455":"ja","subitem_1522300014469":"Other","subitem_1523261968819":"安定ホモトピー"},{"subitem_1522299896455":"ja","subitem_1522300014469":"Other","subitem_1523261968819":"ホモトピーファイバー"},{"subitem_1522299896455":"ja","subitem_1522300014469":"Other","subitem_1523261968819":"インスタントン"},{"subitem_1522299896455":"ja","subitem_1522300014469":"Other","subitem_1523261968819":"リー群"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"rational function"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"completion"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"loop space"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"homology"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"stable homotopy"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"homotopy fiber"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"instanton"},{"subitem_1522299896455":"en","subitem_1522300014469":"Other","subitem_1523261968819":"Lie group"}]},"item_1617186626617":{"attribute_name":"Description","attribute_value_mlt":[{"subitem_description":"科研費番号: 13640085","subitem_description_type":"Other"},{"subitem_description":"平成13年度～平成14年度科学研究費補助金(基盤研究(C)(2))研究成果報告書","subitem_description_type":"Other"},{"subitem_description":"Instantonsのmoduli空間にはそれを開集合として含むUhlenbeck completionがあり,gauge理論において1つの中心的研究手段である.本研究の目的はS^2から複素多様体Vへの有理関数空間に同様の完備化を定義し,その位相幾何を調べることである.\\nまず典型的な場合であるV=CP^nのときを考える.Rat_k(CP^n)でS^2からCP^nへの基点を保つdegree kの正則写像空間を表す.i_k : Rat_k(CP^n)→Ω^2_kCP^n【similar or equal】Ω^2S^<2n+1>を包含写像とする.Segalによりi_κはκ(2n-1)次元までホモトピー同値であり,更に Rat_k(CP^n)の安定ホモトピー型は報告者及びそれとは独立にCohen-Cohen-Mann-Milgramにより,Ω^2S^<2n+1>のstable summandsを用いて記述されていた.\\nRat_k(CP^n)は共通根を持たない monicな複素k次多項式の(n+1)組を表示されるがこれを一般化してX^l_k(CP^n)を高々l個の共通根を持つmonicな複素k次多項式の (n+1)組とする.X^0_k(CP^n)=Rat_k(CP^n)であり,X^k_k(CP^n)=C^<k(n+1)>である.本研究では後者が前者のUhlenbeck完備化であることを証明した.つまりX^l_k(CP^n)はRat_k(CP^n)がその完備化に移行していく空間なのである.更にX^l_k(CP^n)の安定ホモトピー型を決定することに成功した.\\n次にCP_nをloop群ΩGに一般化したときの有理関数空間(これは正にinstantonsのmoduli空間である)の完備化を研究した.研究過程で次のことも分かった.SU(2)のGにおける中心化群を 0とおきJ : G/C→Ω^3_0GをJ(gC)(x)=gxg^<-1>x^<-1>とおく.このときJ_*:H_*(G/C ; Z/2)→H_*(Ω^3_0G ; Z/2)は単射である.この結果はBottによるΩGのgenerating mapsに関する定理の一般化でありこれ自身大変興味あるものである.","subitem_description_type":"Other"},{"subitem_description":"For instanton moduli spaces we have the Uhlenbeck completion, which is useful in the field of gauge theory. The purpose of this study is to define a similar completion for spaces of rational functions from S^2 to a complex manifold V.\\nFirst we study the typical case V = CP^n. Let Rat_k(CP^n) be the space of based holomorphic maps of degree k from S^2 to CP^n. Let i_k : Rat_k(CP^n) → Ω^2_kCP^n 【similar or equal】 Ω^2S^<2n+1> be the inclusion. Segal showed that i_k is a homotopy equivalence up to dimension k(2n - 1). Later I and independently Cohen-Cohen-Mann-Milgram described the stable homotopy type of Rat_k(CP^n) in terms of stable summands of Ω^2S^<2n+1>.\\nNote that Rat_k(CP^n) consists of (n + 1)-tuples of monic degree k complex polynomials without common roots. Generalizing this, we define a space X^l_k(CP^n) by the set of (n + 1)-tuples of monic degree k complex polynomials with at most l roots in common. We have X^0_k(CP^n) = Rat_k(CP^n) and X^k_k(CP^n) = C^<k(n+1)>. In this study I proved that the latter is the Uhlenbeck completion of the former. This implies that X^l_k(CP^n) is a space which appears when we shift from Rat_k(CP^n) to its completion. Moreover, I succeeded in determining the stable homotopy type of X^l_k(CP^n).\\nNext I change CP^n to a loop group ΩG. In this case the space of rational functions from S^2 to ΩG is exactly the instanton moduli space. I studied its completion. In the process of the study, I was able to prove the following theorem: Let C be the centralizer of SU(2) in G and let J : G/C → Ω^3_0 be the map defined by J(gC)(x) = gxg^<-1>x^<-1>. Then J_* : H_*(G/C; Z/2) → H_*(Ω^3_0G; Z/2) is injective. Note that this result is a generalization of the Bott's theorem about generating maps of ΩG, and very interesting in itself.","subitem_description_type":"Other"},{"subitem_description":"未公開：P.7以降（別刷論文のため）","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/20.500.12000/9227"}]},"item_1617186920753":{"attribute_name":"Source Identifier","attribute_value_mlt":[{"subitem_1522646500366":"NCID","subitem_1522646572813":"BA64193961"}]},"item_1617187056579":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2003-03","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":"13640085.pdf","mimetype":"application/pdf","url":{"objectType":"fulltext","url":"https://u-ryukyu.repo.nii.ac.jp/record/2004450/files/13640085.pdf"},"version_id":"3a36e013-f262-4e22-89d6-bf45d037c67d"}]},"item_title":"有理関数空間の完備化の位相幾何","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":"2004450","relation_version_is_last":true,"title":["有理関数空間の完備化の位相幾何"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2022-10-31T01:57:55.447289+00:00"}