The Homotopy Types of Suspended Simply-connected $6$-manifolds

Abstract: Under the assumption that certain Adem cohomology operation acts trivially on $H^2(M;\mathbb{Z}/2)$, we determine the homotopy types of the triple suspension $\Sigma^3M$ of a simply-connected oriented closed topological(or smooth) $6$-manifold $M$, whose integral homology groups can have $2$-torsion.