This article is cited in 30 papers

METHODS OF THEORETICAL PHYSICS

On the defect and stability of differential expansion

Ya. Kononov^a, A. Morozov<sup>bcd

a</sup> Higher School of Economics, Math Department, 117312 Moscow, Russia
^b Institute for Information Transmission Problems, 127994 Moscow, Russia
^c National Research Nuclear University "MEPhI", 15409 Moscow 1, Russia
^d Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia

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.

Received: 30.04.2015

Language: English

DOI: 10.7868/S0370274X15120115

 English version: Journal of Experimental and Theoretical Physics Letters, 2015, 101:12, 831–834

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