Topological properties of black rings

In this paper, we study topological properties of neutral and dipole black rings. Different values of the rings' parameters are used to calculate topological numbers. The topological number for the neutral black ring is unique and independent of its parameters. The topological number for the dipole black ring is parameter dependent. Its topological number is −1 when the parameter N=1 and 3. The topological number can be 0 and 1 when N=2, which is determined by the shape and rotational velocity of the ring. This shows that the parameters of the dipole black ring play an important role in the topological class for the black holes.