| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
The main theme of this research project is to study the algebraic structure of the mapping class group using one-dimensional objects on surfaces. In particular, in connection with the theory of the Johnson homomorphism, we obtain results on the relationship between the algebraic properties of loops on surfaces and the three-dimensional topology, and an explicit formula for some numerical invariant for fatgraph spines. Also, we have improved previous results on the relationship between the topology of loops on surfaces and the Kashiwara-Vergne equation.
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