| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
We characterized some isometries on the continuously differentiable function spaces over compact Riemannian manifolds as generalized weighted composition operators, and illustrated deformations of the isometry groups under norm-perturbations with some concrete manifolds. Some Banach-Stone type theorems were obtained in joint works with S.Oi, H.Koshimizu, O. Hatori and T.Miura. Also we showed that the topological Hochschild cohomology of Lipschitz algebras over compact geodesic spaces is infinite dimensional, which shows a contrast to the fact that global homological dimension of the smooth function algebra over a compact smooth manifold is equal to the dimension of the manifold.
We studied the mean dimension of the shift maps on generalized inverse limits and obtained an estimate in terms of the lengths of periodic blocks. The result was applied to refine the dichotomy on the topological entropy of the shift map discovered by Erceg-Kennedy.
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