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On a conjecture by Kidwell and Stoimenow | | Hermann Gruber
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7 Jun 2004 | | Subject: | Geometric Topology; Quantum Algebra MSC-class: 57M27; 57M25 | math.GT math.QA | | Abstract: | Recently, Stoimenow and Kidwell asked: Let K be a non-trivial knot, and let W(K) be a Whitehead double of K. Let F(a,z) be the Kauffman polynomial and P(v,z) the skein polynomial. Is then always max deg_z P_W(K) - 1 = 2 max deg_z F_K? Here the conjecture is rephrased as an equation in terms of Rudolph’s framed polynomial and the Kauffman polynomial. This equality holds for algebraic alternating links, partially solving at the time a conjecture by Tripp concerning the canonical genus. For the framed polynomial, we show there is a formula for link composition, although there are no known skein relations for it. | | Source: | arXiv, math.GT/0406106 | | Services: | Forum | Review | PDF | Favorites | |
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