Author Summary In this manuscript, we use methods of zigzag homology theory to study the physiological role of the replays—the hippocampal networks endogenous activity that recapitulates the activity of the place cells during exploration of the environment. In particular, we demonstrate that deterioration of the hippocampal spatial memory map caused by excessive transience of synaptic connections may be mitigated by spontaneous replays. The results help to understand how transient information about local spatial connectivity may stabilize at a large scale, and shed light on the separation between faster and slower memory processing in the complementary (hippocampal and neocortical) learning systems. Abstract The spiking activity of the hippocampal place cells plays a key role in producing and sustaining an internalized representation of the ambient space—a cognitive map. These cells do not only exhibit location-specific spiking during navigation, but also may rapidly replay the navigated routs through endogenous dynamics of the hippocampal network. Physiologically, such reactivations are viewed as manifestations of “memory replays” that help to learn new information and to consolidate previously acquired memories by reinforcing synapses in the parahippocampal networks. Below we propose a computational model of these processes that allows assessing the effect of replays on acquiring a robust topological map of the environment and demonstrate that replays may play a key role in stabilizing the hippocampal representation of space.