If a knot is represented by an m‐strand braid, then HOMFLY polynomial in representation R
is a sum over characters in all representations Q∈ R⊗ m. Coefficients in this sum are traces …

A bstract The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-
Simons theory, possess an especially simple representation for torus knots, which begins …

A bstract Character expansion is introduced and explicitly constructed for the (noncolored)
HOMFLY polynomials of the simplest knots. Expansion coefficients are not the knot …

In temporal gauge A0= 0 the 3d Chern–Simons theory acquires quadratic action and an
ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of …

We discuss using the cabling procedure to calculate colored HOMFLY polynomials. We
describe how it can be used and how the projectors and R-matrices needed for this …

A bstract With the help of the evolution method we calculate all HOMFLY polynomials in all
symmetric representations [r] for a huge family of (generalized) pretzel links, which are made …

We review quantum field theory approach to the knot theory. Using holomorphic gauge, we
obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and …

A bstract Many knots and links in S 3 can be drawn as gluing of three manifolds with one or
more four-punctured S 2 boundaries. We call these knot diagrams as double fat graphs …

A bstract Continuing the quest for exclusive Racah matrices, which are needed for
evaluation of colored arborescent-knot polynomials in Chern-Simons theory, we suggest to …

We generalize the recently discovered planar decomposition (Kauffman bracket) for the
HOMFLY polynomials of bipartite knot/link diagrams to (anti) symmetrically colored HOMFLY …