2007 Fiscal Year Final Research Report Summary
New Developments ofAlgebtaic Topology
| Project/Area Number |
16340015
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
MINAMI Norihiko Nagoya Institute of Technology, Faculty of Technobgy, Professor (80166090)
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| Co-Investigator(Kenkyū-buntansha) |
TSUCHIYA Akihiro Nagoya University, Graduate School of Mathematics, Professor (90022673)
FURUTA Mikio Tokyo University, Faculty of MathematicaiScierres, Professor (50181459)
KAMETANI Yukio Keio University, Faculty of Science and Technology, Asscoiate Professor (70253581)
KOBAYASHI Ryoichi Nagoya University, Graduate School of Mathematics, Professor (20162034)
SHIMAKAWA Kazuhisa Okayama University, FacultyofScience, Professor (70109081)
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| Project Period (FY) |
2004 – 2007
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| Keywords | Stable Homotopy / choromatic tower / Obstruction Theory / Equivariant Homotopy Theory / Seiberg-Witten Invariants / Quasi Category / Homotonical Algebraic Geometry / Motif Theory |
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| Research Abstract |
Following some strong demand of the investigator Tsuchiya, the head investigator, Minami embarked upon intensive rematch on the dg-category theory of Keller, Toen, Tabuada, and on the derived algebraic geometry of Toen-Vezzosi and Lurie. Although prominent results are yet to be discovered in these disciplines, some dividends have been obtained to study the Hopkins Chromatic Splitting Conjecture, one of the most fundamental problems in the stable homotopy theory. Also, concerning the fundamental Tate conjecture in the motif theory of algebraic geometry, the head investigator Minami pointed out a fatal mistake in someone's acclaimed solution of the Tate conjecture, and realized a possibly new promising approach to the Tate conjecture.
The investigator Tsuchiya made a big progress in the conformal field theory on the Riemman surface associated with the vertex operator algebra satisfying the C2 condition. The investigators Furuta and Kametani obtained a perhaps, under the current level of algebraic topology, the decisive result on the Bauer-Furuta-Seiberg-Witten invariants when hi is positive. The invesitagator Shimakawa opened up a completely new approach to the compact Lie group equivariant generalized cohomology theories, from the view point of the labeled configuration spaces and continuous functors.
Very recently, the investigator Kobayashi, making full use of Perelman's method, has obtained a series of prominent results, including an affirmative andwer to Lebrun's conjecture. This is a very important achievement which is well beyong the head investigator's initial expectations.
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Research Products
(86 results)
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[Presentation] Model Topos2007
Author(s)
南 範彦
Organizer
Behrens連続講演-準備セミナー
Place of Presentation
岡山大学理学部2号館3階合同演習室(D-301)
Year and Date
2007-12-26
Description
「研究成果報告書概要(和文)」より
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[Presentation] 球の体積と表面積2007
Author(s)
古田 幹雄
Organizer
2007年度 高校生のための現代数学講座
Place of Presentation
東京大学大学院数理科学研究科
Year and Date
2007-07-28
Description
「研究成果報告書概要(和文)」より
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[Presentation] 面積と分数,2007
Author(s)
古田 幹雄
Organizer
2007年度 高校生のための現代数学講座
Place of Presentation
東京大学大学院数理科学研究科
Year and Date
2007-07-21
Description
「研究成果報告書概要(和文)」より
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[Presentation] 連続関手と一般ホモロジー,2006
Author(s)
島川 和久
Organizer
変換群論の手法, RIMS 研究集会
Place of Presentation
京都大学数理解析研究所
Year and Date
2006-05-24
Description
「研究成果報告書概要(和文)」より
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