2006 Fiscal Year Final Research Report Summary
Characterization of the quantum and the finite type link invariants via the algebraic links.
| Project/Area Number |
16540091
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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 | Kurume National College of Technology |
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Principal Investigator |
NAKABO Shigekazu Kurume National College of Technology, General Education of Science, Associate Professor, 一般科目理科系, 助教授 (80259960)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Masaro Kurume National College of Technology, General Education of Science, Associate Professor, 一般科目理科系, 助教授 (70311107)
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| Project Period (FY) |
2004 – 2006
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| Keywords | finite type invariant / quantum invariant / algebraic link / 2-bridge link / Kauffman polynomial / Q-polynomial / Chebyshev ppolynomial |
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| Research Abstract |
There are several approaches to describe the relationships between the finite type invariants and the quantum invariants of knots and links. The main purpose of this research is to characterize the finite type link invariants by the quantum link invariants via the algebraic links.
The author had given explicit formulas of HOMFLY and Jones polynomials for 2-bridge links, which is a family of specific links belonging to the algebraic links. We proceeded to investigate the other quantum invariants for 2-bridge links.
As a result, we had a formula to describe the Q and Kauffman polynomials for 2-bridge links in terms of Chebyshev polynomials, through the computational experiments based on the method given by Lickorish which presents the Q and Kauffman polynomials by matrix manipulations.
It is well-known that he Chebyshev polynomial is deeply related to various areas in mathematical science or engineering, especially the number theory, combinatrics, approximation theory etc. We expect our formulas to connect the different objects or areas to the knot theory.
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Research Products
(2 results)
