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A good command of the theory of principal bundles is essential for mastery of modern differential geometry (cf. , ). In recent years, principal bundles have also become central to key advances in mathematical physics (Yang-Mills theory) which have in turn generated exciting new mathematics (e.g., S. K. Donaldson’s work on differentiable 4-dimensional manifolds , ). This chapter will be a brief introduction to principal bundles.
KeywordsVector Bundle Principal Bundle Holonomy Group Linear Isomorphism Smooth Section
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