| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Outline of Final Research Achievements |
A surface-knot is a closed surface embedded in 4-space. We study many properties of surface-knots from the viewpoint of surface-tangles and local moves. We characterize a surface-knot which has a decomposition of trivial surface-tangles, and prove the splittability of a surface-tangle with fabric structure.
On the other hand, we also study many properties of virtual knots and welded knots which present surface-knots of genus one. We characterize a virtual knot whose 3-state number is zero, and determine the minimal number of colors needed for effective Fox or Dehn colorings for a knot or surface-knot. We also prove that the crossing change and delta-move on a welded knot are both an unknotting operation.
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