On the Ontological Status of Topology Change in Classical Cosmology

The assumption that spacetime topology remains fixed throughout classical evolution is widely treated as a background condition in general relativity and its classical extensions, including Einstein–Cartan theory. However, this assumption is not derived from the local field equations nor supported by any known conservation principle. Instead, it reflects historical and methodological choices made in the early development of relativistic gravity. In this work, we examine the ontological and methodological status of fixed topology in classical cosmology. Drawing on results from modern geometric analysis—most notably the role of surgery in the continuation of Ricci flow—we argue that enforcing global topological invariance can represent a stronger and less clearly justified assumption than allowing controlled topology change once smooth geometric evolution breaks down. From this perspective, topology change need not be interpreted as a dynamical process occurring in time, but rather as a transition between admissible geometric descriptions at the boundary of connected spacetime applicability. We emphasize that relaxing the postulate of fixed topology does not require modifying local gravitational dynamics, introducing new fields, or invoking quantum gravity. Instead, it clarifies the minimal set of assumptions underlying classical gravitational reasoning and delineates the domain in which global connectivity can be consistently maintained. The analysis aims not to advance a specific physical model, but to reassess a rarely examined postulate and to provide a clearer methodological foundation for discussions of singularities, global structure, and classical cosmology.