Study of polynomial invariants of higher dimensional knots
| Project/Area Number |
06640182
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | OSAKA SANGYO UNIVERSITY |
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Principal Investigator |
MARUMOTO Yoshihiko College of general education, Osaka Sangyo University professor, 教養部, 教授 (60136588)
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| Co-Investigator(Kenkyū-buntansha) |
MAKINO Tetsu College of general education, Osaka Sangyo University professor, 教養部, 教授 (00131376)
MURAKAMI Shingo College of general education, Osaka Sangyo University professor, 教養部, 教授 (80028068)
NAGAI Osamu College of general education, Osaka Sangyo University professor, 教養部, 教授 (80029587)
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| Project Period (FY) |
1994 – 1995
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| Project Status |
Completed (Fiscal Year 1995)
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| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1995: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1994: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | knot / polynomial invariant / Link / Ribbon presentation / 絡み輪 |
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| Research Abstract |
We studied about invariants for ditinguishing classic and higher dimensional knots with ribbon presentations.
1. We analyze geometrical position of the life of a knot into the 2-fold branched covering space of a given knot, and we obtain a polynomial invariant from this space which is an invariant of ribbon presentations.
2. The polynomial invariant above is shown to be effective to distinguish known examples of knots each of which has two different ribbon presentations. Those examples were proved to be different by being applied a particular way to prove, and our method however works all those examples. The invariant turns to be valid for studying theta-curve in a 3-space.
3. We generalize a result of a motion group of a trivial link with two components to the case of higher dimensions. Applying our result to the classification of 1-fusion ribbon presentations of knots, we obtain a complete invariant for this.
4. We show the existence of a knot, classic or higher dimensional, that has finitely many different 1-fusion ribbon presentations, and its distinction of those presentations is done by applying the invariant stated in 3.
5. Our invariant in 3 is shown to be valid for the classification of hand-cuff curves in a space. Actually we show a simple calculation of the invariant of sevral examples work well.
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Report
(3 results)
Research Products
(25 results)
