| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
In the study of knots in the 3-space, their complements have played important roles. In fact, the pair of complements of equivalent knots must be homeomorphic. In contrast, Gordon and Luecke have proved that the knots with homeomorphic complements must be equivalent. The key of their proof is an operation called Dehn surgery on knots. Actually, they showed that the trivial and any non-trivial Dehn surgeries on a non-trivial knot give non-homeomorphic pair of 3-manifolds. This theorem can be generalized to the conjecture on knots in general manifolds, which is now called the Cosmetic Surgery Conjecture. In this research project, we have focused on the Dehn surgeries on alternating knots in 3-space, and obtained some partial answer to the conjecture. Also given are some related results on 3-manifolds and knots and links.
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