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arXiv · 1504.07146

On the defect and stability of differential expansion

Ya. Kononov·A. Morozov
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Abstract

Empirical analysis of many colored knot polynomials, made possible by recent computational advances in Chern-Simons theory, reveals their stability: for any given negative N and any given knot the set of coefficients of the polynomial in r-th symmetric representation does not change with r, if it is large enough. This fact reflects the non-trivial and previously unknown properties of the differential expansion, and it turns out that from this point of view there are universality classes of knots, characterized by a single integer, which we call defect, and which is in fact related to the power of Alexander polynomial.

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Ya. Kononov, A. Morozov. 2015-05-07. On the defect and stability of differential expansion. https://doi.org/10.1134/s0021364015120127

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