  We elaborate on the simple alternative from arXiv:1308.5759 to the
matrix-factorization construction of Khovanov-Rozansky (KR) polynomials for
arbitrary knots and links in the fundamental representation of arbitrary SL(N).
Construction consists of 2 steps: first, with every link diagram with m
vertices one associates an m-dimensional hypercube with certain q-graded vector
spaces, associated to its 2^m vertices. A generating function for q-dimensions
of these spaces is what we suggest to call the primary T-deformation of HOMFLY
polynomial -- because, as we demonstrate, it can be explicitly reduced to
calculations of ordinary HOMFLY polynomials, i.e. to manipulations with quantum
R-matrices. The second step is a certain minimization of residues of this new
polynomial with respect to T+1. Minimization is ambiguous and is actually
specified by the choice of commuting cut-and-join morphisms, acting along the
edges of the hypercube -- this promotes it to Abelian quiver, and KR polynomial
is a Poincare polynomial of associated complex, just in the original Khovanov's
construction at N=2. This second step is still somewhat sophisticated -- though
incomparably simpler than its conventional matrix-factorization counterpart. In
this paper we concentrate on the first step, and provide just a mnemonic
treatment of the second step. Still, this is enough to demonstrate that all the
currently known examples of KR polynomials in the fundamental representation
can be easily reproduced in this new approach. As additional bonus we get a
simple description of the DGR relation between KR polynomials and
superpolynomials and demonstrate that the difference between reduced and
unreduced cases, which looks essential at KR level, practically disappears
after transition to superpolynomials. However, a careful derivation of all
these results from cohomologies of cut-and-join morphisms remains for further
studies.
