DAHA和迭代环面结
DAHA and iterated torus knots
摘要：
将DAHA-Jones多项式的理论从环面结推广到其任意迭代（对任意约化的根系和权），包括DAHA超多项式的多项式性、对偶性等性质.假设它们与非负系数情况下的约化稳定Khovanov-Rozansky多项式一致。新的理论很好地匹配了经典理论的代数结和（unibranchise）平面曲线奇异性; Puixix扩展自然出现。相应的DAHA超多项式，预计符合约化的Oblomkov-Shende-Rasmussen猜想后，其推广到任意主导权。例如，构造了a=0，q=1时的DAHA无色超多项式，给出了相应奇点的雅可比因子的贝蒂数.
英文摘要：
The theory of DAHA-Jones polynomials is extended from torus knots to their arbitrary iterations (for any reduced root systems and weights), which incudes the polynomiality, duality and other properties of the DAHA superpolynomials. Presumably they coincide with the reduced stable Khovanov-Rozansky polynomials in the case of non-negative coefficients. The new theory matches well the classical theory of algebraic knots and (unibranch) plane curve singularities; the Puiseux expansion naturally emerges. The corresponding DAHA superpolynomials are expected to coincide with the reduced ones in the Oblomkov-Shende-Rasmussen Conjecture upon its generalization to arbitrary dominant weights. For instance, the DAHA uncolored superpolynomials at a=0, q=1 are conjectured to provide the Betti numbers of the Jacobian factors of the corresponding singularities.
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