| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We establish the theory on compactification of the dynamical moduli spaces for rational functions almost completely. This is one of the main purposes of this research project. Actually, the main purpose is geometric construction of compactification for the deformation spaces of holomorphic branched covering structures and explicit formulation of degeneration and bifurcation of them from the viewpoint of complex geometry. This is acheived for the holomorphic branched covering structure induces by rational functions.
Next, by using cross-ratio coordinates as moduli parameters, not only for finitely generated Moebius groups, but also for iterated function system by contracting self-similarities, we give complete description of the deformation spaces, and clarify the relation between compactification of them and the Teichmuller theory. It is the other main purpose of this project.
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