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On a Background of the Existence of Multi-variable Link Invariants

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We present a quantum theorical background of the existence of multi- variable link invariants, for example the Kauffman polynomial, by observing the quan- tum (sl(2,C), ad)-invariant from the Kontsevich invariant point of view. The background implies that the Kauffman polynomial can be studied by using the sl(N,C)-skein theory similar to the Jones polynomial and the HOMFLY polynomial

Abstract

We present a quantum theorical background of the existence of multi- variable link invariants, for example the Kauffman polynomial, by observing the quan- tum (sl(2,C), ad)-invariant from the Kontsevich invariant point of view. The background implies that the Kauffman polynomial can be studied by using the sl(N,C)-skein theory similar to the Jones polynomial and the HOMFLY polynomial

참고문헌 (12)

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  2. S. V. Chmutov, "Remarks on the Vassiliev knot invariants coming from sl2", Topology, 36, pp.153~178 (1997)
  3. K. Hamai, "A combinatorial reconstruction of the quantum (sl(2,C),ad)-invariant through the Kontsevich invariant (in Japanese, joint work with F. Nagasato)", 석사, pp.2002
  4. C. F. Ho, "A new polynomial for knots and links-preliminary report", Abstracts Amer. Math. Soc, 6, pp.300~ (1985)
  5. T. Kanenobu, "Tangle surgeries on the double of a tangle and link polynomials", Kobe J. Math, 19, pp.19~ (2002)
  6. C. Kassel, "Quantum Groups" (1995), GTM 155, Springer-Verlag
  7. L. H. Kauffman, "On knots, Ann. of Math. Studies", pp.115~ (1987), Princeton University Press
  8. T. T. Q. Le, "Kontsevich's integral for the Kauffman polynomial", Nagoya Math. J, 142, pp.39~65 (1996)
  9. T. T. Q. Le, "The universal Vassiliev-Kontsevich invariant for framed oriented links", Compositio Mathematica, 102, pp.41~46 (1996)
  10. F. Nagasato, "A diagrammatic construction of the (sl(N,C), )-weight system", Inter- isciplinary Information Sciences, 9, pp.43~51 (2003)
  11. T. Ohtsuki, "Quantum Invariants, Series on Knots and Everything", pp.29~ (2002), World Scien-tific
  12. Y. Yokota, "Skeins and quantum SU(N) invariants of 3-manifolds", Math. Ann, 307, pp.109~138 (1997)

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