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stub for universal connection (just to record the references for the moment)
added pointer to:
I have divided the References-section into subsection “In bounded dimension” and “In unbounded dimension”. Then to the first of these I have added these pointers:
Universal connections for manifolds of some bounded dimension $\leq n$ are appealed to in
{#Chern50} Shiing-shen Chern, Differential geometry of fiber bundles, in: Proceedings of the International Congress of Mathematicians, Cambridge, Mass., (August-September 1950), vol. 2, pages 397-411, Amer. Math. Soc., Providence, R. I. (1952) (Chern-DifferentialGeometryOfFiberBundles.pdf:file, full proceedings vol 2 pdf)
(in the context of Chern-Weil theory)
and discussed in detail in
Mudumbai Narasimhan and Sundararaman Ramanan, Existence of Universal Connections, American Journal of Mathematics Vol. 83, No. 3 (Jul., 1961), pp. 563-572 (jstor:2372896 )
Mudumbai Narasimhan and Sundararaman Ramanan, Existence of Universal Connections II, American Journal of Mathematics Vol. 85, No. 2 (Apr., 1963), pp. 223-231 (jstor:2373211)
Roger Schlafly, Universal connections, Invent Math 59, 59–65 (1980) (doi:10.1007/BF01390314)
Roger Schlafly, Universal connections: the local problem, Pacific J. Math. Volume 98, Number 1 (1982), 157-171 (euclid:pjm/1102734394)
also pointer to
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