Infinite Dimensional Path Bundles

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Focusing on the construction of the path bundle, this thesis explores the transition from finite-dimensional principal fiber bundles to infinite-dimensional manifolds of paths. It examines the mapping spaces from a compact interval into the bundle's base space and introduces connections and connection forms, demonstrating the triviality of specific subbundles. The work also analyzes how connections from finite-dimensional bundles influence those on the path bundle, culminating in the definition of curvature terms and a discussion of uniform connections with a practical example.