An associated bundle is a construction from differential geometry and algebraic topology that pertains to the study of fiber bundles. In the context of a fiber bundle, the associated bundle is a way of "associating" a new fiber bundle with a given principal bundle and a representation of its structure group.
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For a principal bundle and a left action of its structure group on a manifold , the associated bundle is , where . Local sections identify it with ; principal transition functions act on . Linear actions give associated vector bundles.