{"_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": "\u6709\u7406\u95a2\u6570\u7a7a\u9593\u306e\u5b8c\u5099\u5316\u306e\u4f4d\u76f8\u5e7e\u4f55", "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": "\u795e\u5c71, \u9756\u5f66", "creatorNameLang": "ja"}]}, {"creatorNames": [{"creatorName": "\u5fd7\u8cc0, \u535a\u96c4", "creatorNameLang": "ja"}]}, {"creatorNames": [{"creatorName": 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"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": "\u79d1\u7814\u8cbb\u756a\u53f7: 13640085", "subitem_description_type": "Other"}, {"subitem_description": "\u5e73\u621013\u5e74\u5ea6\uff5e\u5e73\u621014\u5e74\u5ea6\u79d1\u5b66\u7814\u7a76\u8cbb\u88dc\u52a9\u91d1(\u57fa\u76e4\u7814\u7a76(C)(2))\u7814\u7a76\u6210\u679c\u5831\u544a\u66f8", "subitem_description_type": "Other"}, {"subitem_description": "Instantons\u306emoduli\u7a7a\u9593\u306b\u306f\u305d\u308c\u3092\u958b\u96c6\u5408\u3068\u3057\u3066\u542b\u3080Uhlenbeck completion\u304c\u3042\u308a,gauge\u7406\u8ad6\u306b\u304a\u3044\u30661\u3064\u306e\u4e2d\u5fc3\u7684\u7814\u7a76\u624b\u6bb5\u3067\u3042\u308b.\u672c\u7814\u7a76\u306e\u76ee\u7684\u306fS^2\u304b\u3089\u8907\u7d20\u591a\u69d8\u4f53V\u3078\u306e\u6709\u7406\u95a2\u6570\u7a7a\u9593\u306b\u540c\u69d8\u306e\u5b8c\u5099\u5316\u3092\u5b9a\u7fa9\u3057,\u305d\u306e\u4f4d\u76f8\u5e7e\u4f55\u3092\u8abf\u3079\u308b\u3053\u3068\u3067\u3042\u308b.\\n\u307e\u305a\u5178\u578b\u7684\u306a\u5834\u5408\u3067\u3042\u308bV=CP^n\u306e\u3068\u304d\u3092\u8003\u3048\u308b.Rat_k(CP^n)\u3067S^2\u304b\u3089CP^n\u3078\u306e\u57fa\u70b9\u3092\u4fdd\u3064degree k\u306e\u6b63\u5247\u5199\u50cf\u7a7a\u9593\u3092\u8868\u3059.i_k : Rat_k(CP^n)\u2192\u03a9^2_kCP^n\u3010similar or equal\u3011\u03a9^2S^\u003c2n+1\u003e\u3092\u5305\u542b\u5199\u50cf\u3068\u3059\u308b.Segal\u306b\u3088\u308ai_\u03ba\u306f\u03ba(2n-1)\u6b21\u5143\u307e\u3067\u30db\u30e2\u30c8\u30d4\u30fc\u540c\u5024\u3067\u3042\u308a,\u66f4\u306b Rat_k(CP^n)\u306e\u5b89\u5b9a\u30db\u30e2\u30c8\u30d4\u30fc\u578b\u306f\u5831\u544a\u8005\u53ca\u3073\u305d\u308c\u3068\u306f\u72ec\u7acb\u306bCohen-Cohen-Mann-Milgram\u306b\u3088\u308a,\u03a9^2S^\u003c2n+1\u003e\u306estable summands\u3092\u7528\u3044\u3066\u8a18\u8ff0\u3055\u308c\u3066\u3044\u305f.\\nRat_k(CP^n)\u306f\u5171\u901a\u6839\u3092\u6301\u305f\u306a\u3044 monic\u306a\u8907\u7d20k\u6b21\u591a\u9805\u5f0f\u306e(n+1)\u7d44\u3092\u8868\u793a\u3055\u308c\u308b\u304c\u3053\u308c\u3092\u4e00\u822c\u5316\u3057\u3066X^l_k(CP^n)\u3092\u9ad8\u3005l\u500b\u306e\u5171\u901a\u6839\u3092\u6301\u3064monic\u306a\u8907\u7d20k\u6b21\u591a\u9805\u5f0f\u306e (n+1)\u7d44\u3068\u3059\u308b.X^0_k(CP^n)=Rat_k(CP^n)\u3067\u3042\u308a,X^k_k(CP^n)=C^\u003ck(n+1)\u003e\u3067\u3042\u308b.\u672c\u7814\u7a76\u3067\u306f\u5f8c\u8005\u304c\u524d\u8005\u306eUhlenbeck\u5b8c\u5099\u5316\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u305f.\u3064\u307e\u308aX^l_k(CP^n)\u306fRat_k(CP^n)\u304c\u305d\u306e\u5b8c\u5099\u5316\u306b\u79fb\u884c\u3057\u3066\u3044\u304f\u7a7a\u9593\u306a\u306e\u3067\u3042\u308b.\u66f4\u306bX^l_k(CP^n)\u306e\u5b89\u5b9a\u30db\u30e2\u30c8\u30d4\u30fc\u578b\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u305f.\\n\u6b21\u306bCP_n\u3092loop\u7fa4\u03a9G\u306b\u4e00\u822c\u5316\u3057\u305f\u3068\u304d\u306e\u6709\u7406\u95a2\u6570\u7a7a\u9593(\u3053\u308c\u306f\u6b63\u306binstantons\u306emoduli\u7a7a\u9593\u3067\u3042\u308b)\u306e\u5b8c\u5099\u5316\u3092\u7814\u7a76\u3057\u305f.\u7814\u7a76\u904e\u7a0b\u3067\u6b21\u306e\u3053\u3068\u3082\u5206\u304b\u3063\u305f.SU(2)\u306eG\u306b\u304a\u3051\u308b\u4e2d\u5fc3\u5316\u7fa4\u3092 0\u3068\u304a\u304dJ : G/C\u2192\u03a9^3_0G\u3092J(gC)(x)=gxg^\u003c-1\u003ex^\u003c-1\u003e\u3068\u304a\u304f.\u3053\u306e\u3068\u304dJ_*:H_*(G/C ; Z/2)\u2192H_*(\u03a9^3_0G ; Z/2)\u306f\u5358\u5c04\u3067\u3042\u308b.\u3053\u306e\u7d50\u679c\u306fBott\u306b\u3088\u308b\u03a9G\u306egenerating maps\u306b\u95a2\u3059\u308b\u5b9a\u7406\u306e\u4e00\u822c\u5316\u3067\u3042\u308a\u3053\u308c\u81ea\u8eab\u5927\u5909\u8208\u5473\u3042\u308b\u3082\u306e\u3067\u3042\u308b.", "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) \u2192 \u03a9^2_kCP^n \u3010similar or equal\u3011 \u03a9^2S^\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 \u03a9^2S^\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 \u03a9G. In this case the space of rational functions from S^2 to \u03a9G 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 \u2192 \u03a9^3_0 be the map defined by J(gC)(x) = gxg^\u003c-1\u003ex^\u003c-1\u003e. Then J_* : H_*(G/C; Z/2) \u2192 H_*(\u03a9^3_0G; Z/2) is injective. Note that this result is a generalization of the Bott\u0027s theorem about generating maps of \u03a9G, and very interesting in itself.", "subitem_description_type": "Other"}, {"subitem_description": "\u672a\u516c\u958b\uff1aP.7\u4ee5\u964d\uff08\u5225\u5237\u8ad6\u6587\u306e\u305f\u3081\uff09", "subitem_description_type": "Other"}, {"subitem_description": "\u7814\u7a76\u5831\u544a\u66f8", "subitem_description_type": "Other"}]}, "item_1617186643794": {"attribute_name": "Publisher", "attribute_value_mlt": [{"subitem_1522300295150": "ja", "subitem_1522300316516": "\u795e\u5c71\u9756\u5f66"}]}, "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_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": "\u6709\u7406\u95a2\u6570\u7a7a\u9593\u306e\u5b8c\u5099\u5316\u306e\u4f4d\u76f8\u5e7e\u4f55", "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": ["\u6709\u7406\u95a2\u6570\u7a7a\u9593\u306e\u5b8c\u5099\u5316\u306e\u4f4d\u76f8\u5e7e\u4f55"], "weko_shared_id": -1}