| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
We proposed a conjecture which claims that a 3-manifold group is not bi-orderable if and only if it admits a generalized torsion element. Although this is still open, we solved it for various families of 3-manifolds such as Seifert fibered manifolds. As a byproduct, we found a way to construct generalized torsion elements for Fibonacci groups and their generalizations. Also, we studied the normal closures of slope elements in knot groups and their inclusion relation.
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