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The Kauffman Polynomial and Trivalent Graphs

Carmen Caprau|James Tipton
경북대학교 자연과학대학 수학과|2015.12|Kyungpook Mathematical Journal|제55권 제4호|pp. 779-806

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참고문헌

키워드

Kauffman polynomialbraidsinvariants for graphs and linksknotted graphs
주제분류수학

초록

We construct a state model for the two-variable Kauffman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in R3.

Abstract

We construct a state model for the two-variable Kauffman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in R3.

참고문헌 (12)

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  2. J. S. Birman, "Braids, links and mapping class groups", Annals of Math Study, (82) (1974), Princeton University Press
  3. J. S. Birman., "Braids, link polynomial and a new algebra", Trans. Amer. Math. Soc, 313(1), pp.249~273 (1989)
  4. R. P. Carpentier, "From planar graphs to embedded graphs-a new approach to Kau-man and Vogel's polynomial", J. Knot Theory Rami cation, 9(8), pp.975~986 (2000)
  5. L. H. Kau man, "Invariants of graphs in three-space", Trans. Amer. Math. Soc, 311(2), pp.697~710 (1989)
  6. L. H. Kau man, "An invariant of regular isotopy", Trans. Amer. Math. Soc, 318(2), pp.417~471 (1990)
  7. L. H. Kau man, "Series on Knots and Everything" (2001), World Sci. Pub.
  8. L. H. Kau man., "Link polynomials and a graphical calculus", J. Knot Theory Rami cations, 1, pp.59~104 (1992)
  9. A. Ishii, "Moves and invariants for knotted handlebodies", Algebr. Geom. Topol, 8, pp.1403~1418 (2008)
  10. J. Murakami, "The Kau man polynomial of links and representation theory", Osaka J. Math, 24, pp.745~758 (1987)
  11. H. Murakami., "Hom y polynomial via an invariant of colored plane graphs", L'Enseignement Mathematique, 44, pp.325~360 (1998)
  12. S. Suzuki, "On linear graphs in 3-sphere", Osaka J. Math, 7, pp.375~396 (1970)

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