Topology of charged AdS black hole in restricted phase space

The local topological properties of black hole systems can be expressed through winding numbers as defects. To date, AdS black hole thermodynamics are often depicted by the dual parameters of in the extended phase space, while there have been several studies on the black hole thermodynamics in the restricted phase space. In this paper, we analyze the topological properties of charged AdS black holes in the restricted phase space under the higher-dimension and higher-order curvature gravity frame. The results show that the topological number of the charged black hole in the same canonical ensembles is a constant and is independent of the concrete dual thermodynamical parameters. However, the topological number in the grand canonical ensemble is different from that in the canonical ensemble for the same black hole system. Furthermore, these results are independent of dimension d and highest order k of the Lanczos-Lovelock densities.