| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
A knot is a circle in the 3-dimensional space R3. Two knots are regarded as the same if one is deformed into the other by a continuous deformation of R3 keeping its whole shape. A knot is called trivial if it can be deformed so that it lies in a plane. A trivial knot is a knot which can be untangled. There is an algebra called quandle which has axioms closely related to the elementary moves on knot diagrams. There are many studies on quandle colorings. A quandle coloring assigns elements of a quandle to arcs of a knot diagram so that the crossing condition is satisfied at each crossing. If a knot diagram has only trivial quandle coloring for any quandle, then it represents the trivial knot. Using this fact, we find a finite algorithm to decide a given knot diagram represents the trivial knot. We showed that this algorithm works for all the diagram of the trivial knot with 11 or less number of crossings.
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