Geometric construction of modular functors based on Chern-Simons type theories
Project/Area Number |
23740051
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Geometry
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Research Institution | Shinshu University |
Principal Investigator |
GOMI Kiyonori 信州大学, 学術研究院理学系, 准教授 (00543109)
|
Project Period (FY) |
2011-04-28 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
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Budget Amount *help |
¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2013: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2012: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2011: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
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Keywords | K理論 / ねじれK理論 / 「実」ベクトル束 / 「四元数」ベクトル束 / FKMM不変量 / カイラルベクトル束 / 位相的絶縁体 / 位相的T双対 / 四元数ベクトル束 / 実ベクトル束 / Hermite一般ベクトル束 / 位相的量子場の理論 / Chern-Simons理論 |
Outline of Final Research Achievements |
First, I proved a basic property of the Chern character defined for a finite dimensional model of twisted K-theory, and gave an algebro-topological interpretation of so-called Mickelsson's invariant and its generalization. I also proved topological T-dualities for "Real" circle bundles, etc. Then, we classified "Real" and "Quaternionic" vector bundles in low dimension, and studied in detail the FKMM invariant that plays a basic role in the classification of "Quaternionic" bundles. Moreover, we introduced chiral vector bundles and carried out the same classification as above. We also computed twisted K-thoery to discover a new topological insulating phenomena classified by Z/2.
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Report
(5 results)
Research Products
(28 results)