Connection (composite bundle)

Composite bundles Y → Σ → X {\displaystyle Y\to \Sigma \to X} play a prominent role in gauge theory with symmetry breaking, e.g., gauge gravitation theory, non-autonomous mechanics where X = R {\displaystyle X=\mathbb {R} } is the time axis, e.g., mechanics with time-dependent parameters, and so on. There are the important relations between connections on fiber bundles Y → X {\displaystyle Y\to X} , Y → Σ {\displaystyle Y\to \Sigma } and Σ → X {\displaystyle \Sigma \to X} .

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