  Let $N$ be a complete affine manifold $A^n/\Gamma$ of dimension $n$ where
$\Gamma$ is an affine transformation group and $K(\Gamma, 1)$ is realized as a
finite CW-complex. $N$ has a partially hyperbolic holonomy group if the tangent
bundle pulled over the unit tangent bundle over a sufficiently large compact
part splits into expanding, neutral, and contracting subbundles along the
geodesic flow. We show that if the holonomy group is partially hyperbolic of
index $k$, $k < n/2$, then $\mathrm{cd}(\Gamma) \leq n-k$. Moreover, if a
finitely-presented affine group $\Gamma$ acts on $A^n$ properly discontinuously
and freely with the $k$-Anosov linear group for $k \leq n/2$, then
$\mathrm{cd}(\Gamma) \leq n-k$. Also, there exists a compact collection of
$n-k$-dimensional affine subspaces where $\Gamma$ acts on. The techniques here
are mostly from coarse geometry.
