Let $(B,\Delta,\mathscr{A})$ be a simple affine manifold with singularities and let $(B_{0},\mathscr{A})$ be the underlying integral affine manifold. Then

$$f_{0}:X(B_{0},\mathscr{A})\rightarrow B_{0}$$

is a $T^{n}$ bundle with semi-stable monodromy as in Theorem 2.11. In particular, there is an $2n$-manifold $X$ and a topological semi-stable compactification $X(B_{0},\mathscr{A})\hookrightarrow X$. Furthermore, the topological fibration $f:X\rightarrow B$ obtained is topologically simple.