2012 Fiscal Year Final Research Report
1-parameter family of 1-knot and invariant of surface-knot
| Project/Area Number |
22740039
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Kobe University |
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Principal Investigator |
SATOH Shin 神戸大学, 大学院・理学研究科, 准教授 (90345009)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 結び目理論 |
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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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