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A Formula for the Colored Jones Polynomial of 2-Bridge Knots
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We derive a formula for the colored Jones polynomial of 2-bridge knots. For a twist knot, a more explicit formula is given and it leads to a relation between the degree of the colored Jones polynomial and the crossing number.
Abstract
We derive a formula for the colored Jones polynomial of 2-bridge knots. For a twist knot, a more explicit formula is given and it leads to a relation between the degree of the colored Jones polynomial and the crossing number.
참고문헌 (7)
- G. Burde, "Knots" (1985), Walter de Gruyter & Co.,Berlin
- K. Habiro, "On the quantum sl2 invariants of knots and integral homology spheres", Geometry and Topology Monographs, 4(5), pp.55~68 (2000)
- V. F. R. Jones, "A polynomial invariants for knots via von Neumann algebras", Bull. Amer. Math. Soc, N.S, pp.103~111 (1985)
- A. Kawauchi, "A survey of Knot Theory, Birkhauser Verlag" (1996), Switzerland
- R. Lawrence, "On Habiro's cyclotomic expansions of Ohtsuki invariant ((math.GT", 0501549))
- T. T. Q. Le, "Le, The colored Jones polynomial and A-polynomial of two-bridge knots, (math.GT", 0407521)
- G. Masbaum, "Skein-theoretical derivation of some formulas of Habiro", Algebraic and Geomteric Topology, 3(17), pp.537~556 (2003)
관련 논문AI추천
A recursive formula for the Jones polynomial of 2-bridge links and applications서명수, 이상율, 이은주대한수학회 · 대한수학회지2009 · 제46권 제5호Knots with a Trivial Coefficient PolynomialYasuyuki Miyazawa경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제4호Lower bounds for the number of positive and negative crossings in oriented link diagramsFengchun Lei, Kai Zhang대한수학회 · 대한수학회보2017 · 제54권 제6호Optimistic limits of the colored Jones polynomials조진석, Jun Murakami대한수학회 · 대한수학회지2013 · 제50권 제3호Some Limits of the Colored Jones Polynomials of the Figure-eight KnotHitoshi Murakami경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제3호The Second Reidemeister Moves and Colorings of Virtual Knot Diagrams김윤재, 정명주경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제2호
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