| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
We studied the structure of the Lie algebra of graphs (of Lie types) associated with homology cobordism groups of surfaces.
In joint works with Shigeyuki Morita and Masaaki Suzuki, we investigated the chain complex of the Lie algebra to compute its Euler characteristic by using (super) computers. Our computational results show that there exist many non-trivial odd dimensional rational homology classes of the outer automorphism groups of free groups of ranks up to 11. Some results on Lie algebras of similar types are also obtained. We clarified the structure of the Lie algebra itself up to degree 6 by using symplectic representation theory.
As for the structure of homology cobordism groups, we extended the definition of infinitesimal trace homomorphisms in a joint work with G. Massuyeau for surface cases. We also studied higher dimensional generalizations.
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