| Budget Amount *help |
¥2,450,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥450,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥500,000 (Direct Cost: ¥500,000)
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| Research Abstract |
We described rational homotopy types and mixed Hodge structuresof the moduli of representations with Borel mold over the complex number field for the free algebras. We also investigated topological structures of the representation varieties with Borel mold. In other words, we described topological structures of the moduli of representations explicitly for fundamental cases. We studied a certain class of irreducible representations that is called "thick". We described the moduli of 4-dimensional non-thick irreducible representations for the free group of rank 2. Furthermore, we obtained the degenerated Poincare series of degree 6 for determining the structure of the matrix invariant ring.
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