  Let $M_n$ be the topological moduli space of all parallel n-cables of long
framed oriented knots in 3-space. We construct in a combinatorial way for each
natural number $n>1$ a 1-cocycle $R_n$ which represents a non trivial class in
$H^1(M_n; \mathbb{Z} [x_1,x_2,...,x_1^{-1},x_2^{-1},...])$, where the number of
variables $x_m$ depends on $n$. To each generic point in $M_n$ we associate in
a canonical way an arc {\em scan} in $M_n$, such that $R_n(scan)$ is already a
polynomial knot invariant. We show that $R_3(scan)$ detects the
non-invertibility of the knot $8_{17}$ in a very simple way and without using
the knot group.
  There are two well-known canonical loops in $M_n$ for each parallel n-cable
of a long framed knot $K$: Gramain's loop {\em rot} and the Fox-Hatcher loop
{\em fh}. The calculation of $R_n$ is of at most quartic complexity for these
loops with respect to the number of crossings of $K$ for each fixed $n$. It
follows from results of Hatcher that $K$ is not a torus knot if the rational
function $R_n(fh(K))/R_n(rot(K))$ is not constant for each $n>1$.
  $ \oplus_n R_n$ is a natural candidate in order to separate all classes in
$H_1(M_1;\mathbb{Q}) \cong H_1(M_n;\mathbb{Q})$, and in particular to
distinguish all knot types $\pi_0(M_1)$.
