  In this paper, we investigate the topological numbers for singly rotating
Kerr black holes in arbitrary dimensions and four-dimensional Kerr-Newman black
hole. We show that for uncharged black holes, the rotation parameter has a
significant effect on the topological number, and for rotating black holes, the
dimension of spacetime has a remarkable effect on the topological number too.
In addition, we find that the topological numbers of the four-dimensional Kerr
and Kerr-Newman black holes are the same, which seems to indicate that the
electric charge parameter has no effect on the topological number of rotating
black holes. Our current research provides more evidence that the conjecture
put forward in Wei et al. [Phys. Rev. Lett. 129, 191101 (2022)], according to
which all black hole solutions should be separated into three different
topological classes, is accurate, at least in the pure Einstein-Maxwell gravity
theory.
