| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
(1) We determine the palette numbers of n-colorable torus knots and 2-bridge knots. (2) We introduce the double of a surface-knot via ribbon surface-tangles, and construct a natural map from the set of surface-knots to that of the stable classes of ribbon surface-knots. (3) We characterize the writhe polynomial of a virtual knot by shell moves, and extend it to the case of 2-component virtual links. (4) We prove that the pass move is an unknotting operation for welded knots. (4) We introduce a presentation of the double point set of a diagram of a surface-knot by using a Gauss diagram with trivalent chords, and prove that it recovers the Gauss diagram of the corresponding double decker set of the surface-knot diagram. In particular, we give several properties of the double point set in the case of a 2-dimensional knot.
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