Integral Cohomology Groups of Real Toric Manifolds and Small Covers

For a simplicial complex $K$ with $m$ vertices, there is canonical $\mathbb Z_2^m$-space known as real moment angle R \mathcal Z_K$. In this paper, we consider the quotient spaces $Y=\mathbb Z_K / \mathbb Z_2^{k}$, where pure shellable and Z_2^k \subset Z_2^m$ maximal free action on A typical example of such small cover, cover topological analog toric manifold. We compute integral cohomology group $Y$ by using PL cell decomposition obtained from shelling $K$. addition, Bockstein spectral sequence explicitly.