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Knot contact homology and representations of knot groups

机译:结接触同源性和结组表示

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摘要

We study certain linear representations of the knot group that induce augmentations in knot contact homology. This perspective enhances our understanding of the relationship between the augmentation polynomial and the A-polynomial of a knot. For example, we show that for 2-bridge knots the polynomials agree and that this is never the case for (non-2-bridge) torus knots, nor for a family of 3-bridge pretzel knots. In addition, we obtain a lower bound on the meridional rank of the knot. As a consequence, our results give a new proof that torus knots and a family of pretzel knots have meridional rank equal to their bridge number.
机译:我们研究了导致结接触同源性增加的结组的某些线性表示。这种观点增强了我们对结的扩充多项式和A多项式之间关系的理解。例如,我们表明对于2桥结,多项式是一致的,对于(非2桥)圆环结,也不是3桥椒盐脆饼结族,情况并非如此。此外,我们获得了结子午线等级的下限。结果,我们的结果提供了一个新的证明,即圆环结和椒盐脆饼结族的子午线等级等于其桥数。

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