| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
We consider the mapping class group of an orientable surface. Given a mapping class, we can build its mapping torus which is a fibered 3-manifold. It is known by Thurston that a mapping class is pseudo-Anosov (pA) if and only if its mapping torus is hyperbolic. If we fix a fibered 3-manifold M with the first Betti number greater than 1, there are infinitely many ways to represent M as mapping tori. I consider the so-called magic 3-manifold N which is a hyperbolic 3-manifold with 3 cusps.
I explicitly construct every pA mapping class whose mapping torus is homeomorphic N. By using these pA mapping classes, I study some properties on bi-orderings of the fundamental groups of some hyperbolic fibered 3-manifolds.
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