Algebraic Homology and It's Application
| Project/Area Number |
01540041
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | Kyoto University |
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Principal Investigator |
IWAI Akira Kyoto University Yoshida College Professor, 教養部, 教授 (70026764)
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| Co-Investigator(Kenkyū-buntansha) |
AKIBA Tomoharu Kyoto University Yoshida College Professor, 教養部, 教授 (60027670)
YOSHINO Yuuji Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (00135302)
UE Masaaki Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (80134443)
FUJIKI Akira Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (80027383)
SAITO Hiroshi Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (20025464)
今西 英器 京都大学, 教養部, 助教授 (90025411)
伊達 悦朗 京都大学, 教養部, 助教授 (00107062)
鈴木 敏 京都大学, 教養部, 教授 (60026739)
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| Project Period (FY) |
1989 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1990: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1989: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Twisted conjugacy class / Hasse Principle / Hyperkahler structure / Moment map / Seifert fibered space / Diffeomophism type / Cohen-Macaulay module / Representation of algebras / 代数体の微分 / ザイフェルトファイバ-空間 / ケ-ラ-多様体 / モジュライ空間 |
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| Research Abstract |
In our study we pursued the study of the homology of algebras and related topics. The main results are as follows :
1. Saito proved a Hasse principle on twisted conjugacy classes in the multiplicative group of division algebras, which asserts that the twisted conjugacy classes over an algebraic number field are determined by those over the completions of the number field. 2. Fujiki has shown that on the set of equivalence classes of the representations of the fundamental group of a compact Kahler manifold into a complex reductive algebraic group one can introduce a natural structure of a hyperkahler manifold ; more over, in the corresponding Calabi family the two special fibers are isomorphic, via the Hitchin correspondence, to the moduli space of stable Higgs bundle corresponding to the representations [2]. 3. Ue showed that the diffeomorphism types of the Seifert fibered 4-manifolds over the euclidean base orbifolds are determined by their fundamental groups and gave the correspondence between them and certain four types of geometries [4], and also showed similar results for the cases when the basse orbifolds are not euclidean. He gave the decompositions of simply connected elliptic surfaces as 4-manifolds along some Brieskorn homology spheres concretely in different two way. He also constructed the involutions on the elliptic surfaces which reverse the orientations of the fibers and base apaces. 4. Yoshino determined the Cohen-Macaulay representation type for certain Cohen-Macaulay local rings, and has studied, from the algebraic point of view, the relation between singularities and Cohen-Macualay representation types.
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Report
(3 results)
Research Products
(22 results)
