Thermodynamic Topology of Quantum Corrected AdS-Reissner-Nordstrom Black Holes in Kiselev Spacetime

In this paper, we delve into the intricate thermodynamic topology of quantum-corrected Anti-de Sitter-Reissner-Nordstrm (AdS-RN) black hole within the framework of Kiselev spacetime. By employing the generalized off-shell Helmholtz free energy approach, we meticulously compute the thermodynamic topology of these selected black holes. Furthermore, we establish their topological classifications. Our findings reveal that quantum correction terms influence the topological charges of black holes in Kiselev spacetime, leading to novel insights into topological classifications. Our research findings elucidate that, in contrast to the scenario in which $\omega=0$ and $a=0.7$ with total topological charge $W=0$ and $\omega=-4/3$ with total topological charge $W=-1$, in other cases, the total topological charge for the black hole under consideration predominantly stabilizes at +1. This stabilization occurs with the significant influence of the parameters a, c, and $\omega$ on the number of topological charges. Specifically, when $\omega$ assumes the values of $\omega=-1/3$, $\omega=-2/3$ , $\omega=-1$, the total topological charge consistently be to W = +1.