论{\it量子}的几何基础结的A-多项式

Dmitry Galakhov, Alexei Morozov
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摘要

在准经典极限中,它与广为人知的增量理论和接触几何学密切相关。量子化可以用简单得多的术语来表述,从而使这些技术为更多的听众所接受。为了避免过多介绍,本文只考虑了三叶结的着色琼斯多项式的情况,尽管各种概括都很直接。仅限于琼斯多项式(而不是完整的 HOMFLY-PT)与使用考夫曼微积分所提供的严重简化有关。然而,超越琼斯多项式看起来很现实,但它仍然是一个既具有挑战性又充满希望的问题。
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On geometric bases for {\it quantum} A-polynomials of knots
A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum $A$- and $C$-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid overloading of the presentation, only the case of the colored Jones polynomial for the trefoil knot is considered, though various generalizations are straightforward. Restriction to solely Jones polynomials (rather than full HOMFLY-PT) is related to a serious simplification, provided by the use of Kauffman calculus. Going beyond looks realistic, however it remains a problem, both challenging and promising.
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