We characterize the spherical topology of black holes in a special case of spherical symmetry. For this purpose, we carefully consider the metrics space of topological black holes B4. By adjusting some of the parameters, we infer the appropriate components and the equatorial geodesics on the line element of the topological black holes. We also construct the minimum retraction ρ2:B4→ C 3 2. As a result, the minimum deformation retract has also been inferred to explain the effects on their center of mass in binary system. This would help us to better understand some of possible applications in astrophysics and the Cosmology, such as the natural phenomena of merging two black holes and curved the space-time in general relativity. In addition, we find the relation between limit folding and limit minimum retraction on the n-dimension. The folding on connected sum of essential sub-manifolds of the topological black hole have constructed for different types and characteristics.
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