  In this work, we explore the thermodynamic topology of phantom AdS black
holes in the context of massive gravity. To this end, we evaluate these black
holes in two distinct ensembles: the canonical and grand canonical ensembles
(GCE). We begin by examining the topological charge linked to the critical
point and confirming the existence of a conventional critical point $(CP_{1})$
in the canonical ensemble (CE), this critical point has a topological charge of
$-1$ and acts as a point of phase annihilation, this situation can only be
considered within the context of the classical Einstein-Maxwell (CEM) theory
$(\eta=1)$, while no critical point is identified in the GCE. Furthermore, we
consider black holes as a topological defect within the thermodynamic space. To
gain an understanding of the local and global topological configuration of this
defect, we will analyze its winding numbers, and observe that the total
topological charge in the CE consistently remains at $1$. When the system
experiences a pressure below the critical threshold, it gives rise to the
occurrence of annihilation and generation points. The value of electric
potential determines whether the total topological charge in the GCE is zero or
one. As a result, we detect a point of generation point or absence of
generation/annihilation point. Based on our analysis, it can be inferred that
ensembles significantly impact the topological class of phantom AdS black holes
in massive gravity.
