universal connection



\infty-Chern-Weil theory

Differential cohomology



For GG a compact Lie group there is a way to equip the topological classifying space BGB G with smooth structure such that the corresponding smooth universal principal bundle EGBGE G \to B G carries a smooth connection univ\nabla_{univ} with the property that for every GG-principal bundle PXP \to X with connection \nabla there is a smooth representative f:XBGf : X \to B G of the classifying map, such that (P,)(P,f * univ)(P, \nabla) \simeq (P, f^* \nabla_{univ}). This univ\nabla_{univ} is called the universal GG-connection.


  • M. S. Narasimhan and S. Ramanan,

    Existence of universal connections , Amer. J. Math. 83 (1961), 563–572. MR 24 #A3597

    Existence of universal connections II , Amer. J. Math. 85 (1963), 223–231. MR 27 #1904

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