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tried to polish a bit the matrial at Chern-Weil theory.
(not that there is much, yet, but still)
I pasted some historical comments and references (but still incomplete currently) provided by Jim Stasheff into Chern-Weil theory. More to come.
Yet more ancient references, this time kindly dug out by Alan Hatcher.
I have expanded the Idea-section at Chern-Weil theory, giving a more detailed survey of the main constructions.
(this is a spin-off of me staring to write an “Introduction and Survey”-section on my personal web at infinity-Chern-Simons theory (schreiber))
I have finally dug through the original citations for the “Chern-Weil” constructions. Have added the following to the entry:
The differential-geometric “Chern-Weil”-construction (evaluating curvature 2-forms of connections in invariant polynomials) is due to
and around equation (10) of:
It is the independence of this construction under the choice of connection which Chern 50 atributes (below (10)) to
But the main result of Chern 50 is that this differential-geometric “Chern-Weil” construction is equivalent to the topological (homotopy theoretic) construction of pulling back the universal characteristic classes from the classifying space $B G$ along the classifying map of the given principal bundle:
This claim is equation (15) in Chern 50, using (quoting from the same page):
methods initiated by E. Cartan and recently developed with success by H. Cartan, Chevalley, Koszul, Leray, and Weil [13]
Here reference 13 is:
Later, an independent proof of the universal topological “Chern-Weil”-construction $inv(\mathfrak{g}) \to H^\bullet(B G)$ is given in:
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