| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Outline of Final Research Achievements |
The main object of this research project was the Turaev cobracket which is a topological operation measuring the self-intersections of curves on surfaces. In particular, we studied the relationship between the Kashiwara-Vergne problem in Lie theory and the Turaev cobracket. As a result, we established the formality property of the Turaev cobracket and obtained its application to the theory of the Johnson homomorphisms.
We also studied generalized Dehn twists, which is a certain algebraic construction associated to any closed curves on surfaces. In particular, we tried to clarify a geometric interpretation of generalized Dehn twists and partially succeeded in the sense that we obtained a first approximation of them in terms of homology cylinders.
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