What concept describes the universe's overall connectivity, distinct from local geometry?

Topology

Topology is the concept that describes the fundamental connectivity and overall structure of space, addressing whether the universe is globally finite or infinite, irrespective of its local geometric characteristics like curvature. While geometry, defined by curvature, dictates how distances are measured and how triangles behave locally, topology addresses the universe's large-scale configuration—specifically, if space loops back onto itself. A critical example illustrating the difference is that a universe could possess zero curvature (geometrically flat), yet still be topologically finite if it wraps around, as in the case of a torus. Conversely, a simple sphere is finite both geometrically (positive curvature) and topologically. Cosmologists search for repeating patterns in the CMB, which would be evidence of a finite, self-connecting topology.