 Principal bundle

A principal $G$-bundle is a fiber bundle $\pi :P\to B$ with a free right action of a Lie group $G$ that is locally equivariantly isomorphic to $U\times G\to U$. Each fiber is a single $G$-orbit.

A **principal bundle** is a mathematical structure used extensively in geometry and topology, particularly in the fields of differential geometry, algebraic topology, and theoretical physics. It provides a formal framework to study spaces that have certain symmetry properties. Here are the key components and concepts related to principal bundles: ### Components of a Principal Bundle 1. **Base Space (M)**: This is the manifold (or topological space) that serves as the "base" for the bundle.