In this paper, we explore the topological numbers of the rotating charged AdS black holes in four- and five-dimensional gauged supergravity theories within the framework of the thermodynamical topological approach to black holes, adopting the generalized off-shell Helmholtz free energy. We demonstrate that the number of the rotation parameters has a considerable effect on the topological numbers of the five-dimensional rotating AdS black holes. Furthermore, we indicate that the topological numbers of the four- and five-dimensional rotating AdS black holes are blind to the number of the electric charge parameters.
Comment: 10 pages, 10 figures, 1 table, revtex4-1.cls. arXiv admin note: substantial text overlap with arXiv:2307.02030, arXiv:2402.00106