Equivariant homotopy theory and gauge theory
| Project/Area Number |
16540079
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Keio University |
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Principal Investigator |
KAMETANI Yukio Keio University, Faculty of Science and Technology, Assistant Professor, 理工学部, 助教授 (70253581)
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| Co-Investigator(Kenkyū-buntansha) |
FURUTA Mikio University of Tokyo, Graduate School of Mathematical Sciences, Professor, 数理科学研究科, 教授 (50181459)
MAEDA Yoshiaki Keio University, Faculty of Science and Technology, Professor, 理工学部, 教授 (40101076)
MORIYOSHI Hitoshi Keio University, Faculty of Science and Technology, Assistant Professor, 理工学部, 助教授 (00239708)
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| Project Period (FY) |
2004 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | gauge theory / homotopy theory |
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| Research Abstract |
In Seiberg-Witten theory M.Furuta has introduced a finite dimensional approximation to capture the equation in equivariant homotopy theory, by which he has obtained a refinement of the invariant and the 10/8-inequality for closed spin 4-manifolds.
In this research we improved this inequality by taking into account the quadruple structure on one dimensional cohomology. More precisely we defined a variant of KO-characteristics for closed spin 4-manifoldfs and obtained an additional term determined by this invariant. We also showed that, if the quadruple structure is congruent to the one of 4-dimesional torus or the connected sum of its copies modulo 2, our improvement can be estimated. The researcher was reported by M.Furuta that he is now applying this result to study Seiberg-Witten invariants for symplectic 4-manifolds.
After finishing this work we considered how our result is related to geometry of the moduli space of solutions to the equation. Originally this was studied by P.Kroneheimer, who considered this for low-dimensional moduli spaces. To extend his method to higher dimensional moduli spaces, we introduced a sort of KO-characteristics on the moduli space. Then the 10/8-inequality, as well as the above improvement, can be directly obtained from symmetry of the moduli space with its spin structure. Now we are trying to apply this method in other situations as Yang-Mills theory.
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Report
(3 results)
Research Products
(10 results)
