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Cabling procedure for the colored HOMFLY polynomials. (English. Russian original) Zbl 1318.81055
Theor. Math. Phys. 178, No. 1, 1-58 (2014); translation from Teor. Mat. Fiz. 178, No. 1, 3-68 (2014).
In a truly tour de force the authors have discussed how to calculate the so-called colored HOMFLY polynomials via the cabling procedure. Along the whole paper, the reader can find several important procedures necessary to the calculation of HOMFLY polynomials dividing into, basically, three steps: the construction of cable knot from the initial knot, identification of the necessary projector relating fundamental HOMFLY polynomials to colored HOMFLY polynomials, and finally calculation of the colored HOMFLY polynomials.
The paper is well written and the mathematical aspects are presented in a robust and precise manner. Those readers who are interested in topological field theories endowed with $$\mathrm{SU}(N)$$ gauge groups shall find in this paper a solid piece of work supporting future researches in the field.

##### MSC:
 81T45 Topological field theories in quantum mechanics 81T13 Yang-Mills and other gauge theories in quantum field theory 57M25 Knots and links in the $$3$$-sphere (MSC2010)
Knot Atlas
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