Project/Area Number  06640182 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
Geometry

Research Institution  OSAKA SANGYO UNIVERSITY 
Principal Investigator 
MARUMOTO Yoshihiko College of general education, Osaka Sangyo University professor, 教養部, 教授 (60136588)

CoInvestigator(Kenkyūbuntansha) 
牧野 哲 大阪産業大学, 教養部, 教授 (00131376)
村上 信吾 大阪産業大学, 教養部, 教授 (80028068)
永井 治 大阪産業大学, 教養部, 教授 (80029587)
MAKINO Tetsu College of general education, Osaka Sangyo University professor
NAGAI Osamu College of general education, Osaka Sangyo University professor
MURAKAMI Shingo College of general education, Osaka Sangyo University professor

Project Fiscal Year 
1994 – 1995

Project Status 
Completed(Fiscal Year 1995)

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)

Keywords  knot / polynomial invariant / Link / Ribbon presentation / 結び目 / 多項式不変量 / 絡2,輪 / リボン表示 / 絡み輪 
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 2fold 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 thetacurve in a 3space. 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 1fusion 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 1fusion 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 handcuff curves in a space. Actually we show a simple calculation of the invariant of sevral examples work well.
