The coloured Jones function and Alexander polynomial for torus knots
1995 ◽
Vol 117
(1)
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pp. 129-135
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AbstractIn [2] it was conjectured that the coloured Jones function of a framed knot K, or equivalently the Jones polynomials of all parallels of K, is sufficient to determine the Alexander polynomial of K. An explicit formula was proposed in terms of the power series expansion , where JK, k(h) is the SU(2)q quantum invariant of K when coloured by the irreducible module of dimension k, and q = eh is the quantum group parameter.In this paper I show that the explicit formula does give the Alexander polynomial when K is any torus knot.
2004 ◽
Vol 15
(06)
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pp. 547-555
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2003 ◽
Vol 12
(04)
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pp. 463-491
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1999 ◽
Vol 08
(08)
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pp. 1009-1048
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1973 ◽
Vol 6
(9)
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pp. L240-L242
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1993 ◽
Vol 196
(2)
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pp. 283-312
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2011 ◽
Vol 20
(12)
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pp. 1723-1739
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