扭纽结的超A-多项式
Super-A-polynomials for Twist Knots
摘要：
我们猜想了一类扭纽结$K_p$的着色超多项式公式，其中p表示全扭数.通过微分和取特殊极限检验了公式的正确性。利用这些公式，我们计算了小p值扭结的经典和量子超A-多项式，结果支持了广义体积猜想和量子体积猜想的分类版本.进一步证明了在扭纽结的情况下，Q变形的A多项式可以与纽结接触同调的增广多项式一致。
英文摘要：
We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed A-polynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.
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