Ehresmann connection

An Ehresmann connection is a mathematical concept used in differential geometry and the study of fiber bundles. It provides a way to describe a manifold's geometric structure by introducing a "connection" that enables us to compare tangent spaces at different points. Think of it like having a roadmap for navigating surfaces: it allows us to understand how to "move" smoothly across a curved space. This connection helps analyze properties like curvature and parallel transport, which are essential in fields such as theoretical physics, including general relativity, where it aids in understanding the geometry of spacetime.