| Budget Amount *help |
¥15,340,000 (Direct Cost: ¥11,800,000、Indirect Cost: ¥3,540,000)
Fiscal Year 2017: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
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| Outline of Final Research Achievements |
The surface theory and the theory of 3-manifold are linked each other. The aim of this study is to deepen understandings between them especially on invariants of mapping classes, separability of subgroups and computing in topology. In particular, we would have liked to develop comparisons of invariants of mapping classes which do not depend on the topology of surfaces. We then have proved that the normalized entropy of a pseudo-Anosov over the volume of its mapping torus is uniformly bounded from below by some explicit positive constant.
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