增广、环带与Alexander多项式
Augmentations, annuli, and Alexander polynomials
AI总结：
本研究在纽结接触同伦框架下，通过增广簇给出纽结Alexander多项式的新表达式，结合全纯曲线计数与模空间边界分析推导公式，建立了接触同伦与经典纽结不变量的联系。
摘要：
纽结的增广簇是纽结接触同伦微分分次代数的三维系数空间中，该代数允许到复数域的单位链映射的轨迹。我们阐释了如何用增广簇表达纽结的Alexander多项式：它是两个偏导数比值的积分的指数。该表达式源自两种推导：一是将Alexander多项式描述为欧几里得3维空间余切丛中，具有纽结补拓扑的拉格朗日子流形与零截面之间的Floer条带和全纯环带的计数；二是对带一个正穿刺的此类环带的模空间边界的描述。
英文摘要：
The augmentation variety of a knot is the locus, in the 3-dimensional coefficient space of the knot contact homology dg-algebra, where the algebra admits a unital chain map to the complex numbers. We explain how to express the Alexander polynomial of a knot in terms of the augmentation variety: it is the exponential of the integral of a ratio of two partial derivatives. The expression is derived from a description of the Alexander polynomial as a count of Floer strips and holomorphic annuli, in the cotangent bundle of Euclidean 3-space, stretching between a Lagrangian with the topology of the knot complement and the zero-section, and from a description of the boundary of the moduli space of such annuli with one positive puncture.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
