2002 Fiscal Year Final Research Report Summary
Research for Higher-Dimensional Knot Invariants by using Computers
| Project/Area Number |
12640096
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Osaka Sangyo University |
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Principal Investigator |
MARUMOTO Yoshihiko Osaka Sangyo University, College of General Education, Professor, 教養部, 教授 (60136588)
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| Co-Investigator(Kenkyū-buntansha) |
TAMURA Makoto Osaka Sangyo University, College of General Education, Lecturer, 教養部, 講師 (40309175)
HARIKAE Toshio Osaka Sangyo University, College of General Education, Associate Professor, 教養部, 助教授 (50309176)
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| Project Period (FY) |
2000 – 2002
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| Keywords | knot / link / spatial graph / invariant / fundamental group / homotopy group / computer / network system |
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| Research Abstract |
We studied geometrical and algebraic propertied of knots, links and graphs, which are embedded in a space, and we constructed a computational and network environment for the research.
1. We give a characterization of 2^<nd> homotopy group of a ribbon 2-knot under a certain geometrical condition, and discuss the characterization and "ribbon disk conjecture".
2. We introduce a "banded knot", and show geometrical properties of the knot, which turns out to be similar to those of ribbon knots.
3. We characterize the triviality of a bouquet in a space, and study the tunnel number of knots and links in terms of spatial graphs.
4. We study a group structure of a knot group as an automatic group, and continue studing relationships of geometrical and algebraic structures of thess groups.
5. We construct and set up WEB server and Mailing server in the network in the campus, and the servers are open for low-dimensional topology researchers.
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Research Products
(14 results)
