| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Research Abstract |
We study many properties of knotted surfaces in Euclidian 4-space; in particular, we prove the triviality of the quandle cocycle invariant of s roll-spun knot, and the existence of a 2-knot for which any 7-coloring requires at lest 6 colors. On the other hand, a knotted torus in 4-space is closely related to a virtual knot. We also study many properties of virtual knots such as two kinds of crossing numbers, n-writhes, and the upper and lower knot groups.
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