The Integer Coefficents Homology Group Of Small Covers Over L?bell Polyhedron R_?6?and 4-dimensional Cube

Let Mn is a small covers overs simple convex polyhedron Pn,denoted by ?:Mn?Pn.h is a Morse funtion overs Pn,then the cell decomposition and a cellular chain complex of Mn are given by h.According to calculate the boundary homomorphism of the cellular chain complex,we can calculate the homology group of small covers Mn over Pn.In this paper,we calculated the homology group of integral coefficients of small covers over Lobell polyhedron R(6)and 4-dimensional cube.Applying our result to 4-dimensional cube we have that the homology group of small covers over 4-dimensional cube is torsion-free or 2-torsion.