| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
Surface knots were studied using quandle algebras and the following main results were obtained. (1) We explored a diagrammatic relation between biquandle colorings and quandle colorings, and showed that various invariants including coloring numbers are equivalent. (2) We gave a lower bound for the bridge indices of surface knots by using kei coloring numbers, and determined the explicit values for some specific examples. (3) We introduced the shifting chain map on quandle homology theory and explored a relation between quandle cocycle invariants and shadow cocycle invariants. We also observed the induced homomorphism. (4) We studied the knot quandles of knotted spheres, called twist-spun knots, and gave a example of knotted spheres with the same knot group but different knot quandles.
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