| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
It is known that on compact Kahler manifolds, there is a correspondence between flat vector bundles and Higgs bundles so called non-abelian Hodge decomposition.But the non-abelian Hodge decomposition on non-kahler manifolds is not known. In this research, I was constructing the theory of non-abelian Hodge decomposition on non-kahler manifolds by using Twistor structure theory (a generalization of Hodge theory) and Bott-CHern cohomology theory. An important application of this research is to prove that the non-abelian Hodge decomposition exists on compact Sasakian manifolds (an important class of non-kohler manifold). More precisely, I proved that on compact Sasakian manifolds there exists a correspondence between semi-simple flat vector bundles and poly-stable basic Higgs bundles.
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