| Budget Amount *help |
¥10,790,000 (Direct Cost: ¥8,300,000、Indirect Cost: ¥2,490,000)
Fiscal Year 2018: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2017: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2016: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2015: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
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| Outline of Final Research Achievements |
As joint works of the members of our research team, we obtained the following results concerning the cohomology groups of moduli spaces of Riemann surfaces and graphs:
(1) We gave another proof of Bartholdi's result on the 11th rational homology group of the moduli space of graphs of rank 7. (2) We determined the structure of the Lie algebra of Johnson images up to degree 7. (3) We compared certain two filtrations of the Torelli group up to degree 6. This result provides a new insight on the finite type invariants of homology 3-spheres. Also, we determined the rational abelianization of the Johnson kernel. (4) In a joint work with Gwenael Massuyeau, we proved that the rational abelianization of the homology cobordism group of surfaces is non-trivial.
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