Chebyshev polynomials and the Frohman-Gelca formula
Chebyshev polynomials and the Frohman-Gelca formula
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DOI：
10.1142/s0218216515500236
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发表时间：
2014-03
影响因子：
0.5
通讯作者：
Hoel Queffelec;Heather M. Russell
中科院分区：
文献类型：
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作者：
Hoel Queffelec;Heather M. Russell
C. Frohman和R. Gelca利用Chebyshev多项式引入了环面的Kauffman托架串模的一个基础。这个基础特别有用，因为琼斯-考夫曼积可以通过一个非常简单的乘积和公式来描述。本文给出了这个公式的图解证明，强调并揭示了切比雪夫多项式所起的作用。
Using Chebyshev polynomials, C. Frohman and R. Gelca introduced a basis of the Kauffman bracket skein module of the torus. This basis is especially useful because the Jones–Kauffman product can be described via a very simple Product-to-Sum formula. Presented in this work is a diagrammatic proof of this formula, which emphasizes and demystifies the role played by Chebyshev polynomials.