Defect and degree of the Alexander polynomial

نویسندگان

چکیده

Defect characterizes the depth of factorization terms in differential (cyclotomic) expansions knot polynomials, i.e. non-perturbative Wilson averages Chern-Simons theory. We prove conjecture that defect can be alternatively described as degree $q^{\pm 2}$ fundamental Alexander polynomial, which formally corresponds to case no colors. also pose a question if these polynomials arbitrary integer given degree. A first attempt answer latter is preliminary analysis antiparallel descendants 2-strand torus knots, provide nice set examples for all values defect. The turns out positive zero what observed already twist knots. This proved allows us complete $C$-polynomials symmetrically colored zero. In this case, we achieve separation representation and variables.

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ژورنال

عنوان ژورنال: European Physical Journal C

سال: 2022

ISSN: ['1434-6044', '1434-6052']

DOI: https://doi.org/10.1140/epjc/s10052-022-10969-8