{"_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", "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^\u003c2n+1\u003e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^\u003c2n+1\u003e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^\u003ck(n+1)\u003e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^\u003c-1\u003ex^\u003c-1\u003e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^\u003c2n+1\u003e 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^\u003c2n+1\u003e.\\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^\u003ck(n+1)\u003e. 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^\u003c-1\u003ex^\u003c-1\u003e. 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\u0027s 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", "download_preview_message": "", "file_order": 0, "filename": "13640085.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "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"], "permalink_uri": "http://hdl.handle.net/20.500.12000/9227", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2009-03-17"}, "publish_date": "2009-03-17", "publish_status": "0", "recid": "2004450", "relation": {}, "relation_version_is_last": true, "title": ["有理関数空間の完備化の位相幾何"], "weko_shared_id": -1}