Dimensional structure of thermodynamic topology in ultraspinning Kerr-AdS black holes

Abstract: In this paper, we apply the thermodynamic topology framework to ultraspinning Kerr-AdS black holes in arbitrary spacetime dimensions. By constructing the off-shell Helmholtz free energy and the associated vector field, black hole states are characterized as topological defects, and their phase structures are described through zero points, winding numbers, and asymptotic thermodynamic behavior. Analyses of the four- and five-dimensional cases highlight the differences between even- and odd-dimensional configurations, while representative higher-dimensional cases confirm that no additional topological classes or subclasses emerge. We find that only two thermodynamic topological structures appear: the standard class $W^{1+}$ for most configurations, and the distinct subclass $\tilde{W}^{1+}$ for odd-dimensional black holes with maximal rotations. These results establish a unified, dimension-independent classification scheme for ultraspinning Kerr-AdS black holes.