  We prove that if $M$ is a CW-complex, then the homotopy type of the skeletal
filtration of $M$ does not depend on the cell decomposition of $M$ up to wedge
products with $n$-disks $D^n$, when the later are given their natural
CW-decomposition with unique cells of order 0, $(n-1)$ and $n$; a result
resembling J.H.C. Whitehead's work on simple homotopy types. From the Colimit
Theorem for the Fundamental Crossed Complex of a CW-complex (due to R. Brown
and P.J. Higgins), follows an algebraic analogue for the fundamental crossed
complex $\Pi(M)$ of the skeletal filtration of $M$, which thus depends only on
the homotopy type of $M$ (as a space) up to free product with crossed complexes
of the type $\Pi(D^n), n \in N$. This expands an old result (due to J.H.C.
Whitehead) asserting that the homotopy type of $\Pi(M)$ depends only on the
homotopy type of $M$. We use these results to define a homotopy invariant $I_A$
of CW-complexes for any finite crossed complex $A$. We interpret it in terms of
the weak homotopy type of the function space $TOP((M,*),(|A|,*))$, where $|A|$
is the classifying space of the crossed complex $A$.
