  We consider the classical problem of a position of n-dimensional manifold M
in R^{n+2}. We show that we can define the fundamental (n+1)-cycle and the
shadow fundamental (n+2)-cycle for a fundamental quandle of a knotting M to
R^{n+2}. In particular, we show that for any fixed quandle, quandle coloring,
and shadow quandle coloring, of a diagram of M embedded in R^{n+2} we have
(n+1)- and (n+2)-(co)cycle invariants (i.e. invariant under Roseman moves). We
speculate on a similar construction for general Yang-Baxter operators.
