  In this paper, we study topological numbers for five-, six- and
seven-dimensional anti-de Sitter black holes in the ghost-free massive gravity.
We find that when the black holes are charged, they have the same topological
number. The topological numbers for the uncharged black holes are 0 or 1, and
the specific values are determined by the values of the black holes'
parameters. Since $k$ and $c_ 0^2c_2 m^2 $ appear together in the generalized
free energy in the form of $k +c_ 0^2c_2 m^2 $, where $k$ characterizes the
horizon curvature and $c_2 m^2 $ is the coefficient of the second term of
massive potential associated with the graviton mass, this result is applicable
to the black holes with the spherical, Ricci flat or hyperbolic horizons. This
work shows that the parameters of the ghost-free massive gravity play an
important role in topological classes of black holes.
