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On the defect and stability of differential expansion

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arxiv 1504.07146 v3 pith:3RKGNB5Q submitted 2015-04-27 hep-th math.GT

classification hep-thmath.GT
keywords defectdifferentialexpansionfactgivenknotpolynomialstability
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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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  1. Two roles of Alexander in two Kashaev phases

    hep-th 2026-05 unverdicted novelty 5.0 of 10

    Alexander polynomials appear in two opposite roles in two Kashaev phases of Chern-Simons theory due to co-existing branches in the quasiclassical limit with non-trivial versus vanishing classical actions.

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