On spherical fibrations and Poincare complexes

In this paper, we prove that certain spherical fibrations over certain CW-complexes are stably fibre homotopy equivalent to $\text{mm}TOP$-spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for whether a Poincar$\text{mm}\acute{e}$ complex is of the homotopy type of a topological manifold. Moreover, we present the classification for some highly connected manifolds by the homotopy types of highly connected Poincar$\text{mm}\acute{e}$ complexes.