| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
There are two methods of representing 2-dimensional knots in the 4-sphere, using marked graphs in the 3-sphere, and using projections into the 3-sphere. I constructed homological invariants for 2-dimensional knots in the 4-sphere using these two representations. Calculating these homologies explicitly, it was shown that both distinguish the 0-twist spun-trefoil knot from the 2-twist spun-trefoil knot.
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