added pointer to:

- Loring Tu,
*Differential Geometry – Connections, Curvature, and Characteristic Classes*, Springer 2017 (ISBN:978-3-319-55082-4)

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

- Henri Cartan, Section 7 of:
*Notions d’algébre différentielle; applications aux groupes de Lie et aux variétés où opère un groupe de Lie*, Coll. Topologie Algébrique Bruxelles (May 1950) 15-28 (numdam:SHC_1949-1950__2__A18_0)

and around equation (10) of:

- {#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) (pdf)

It is the independence of this construction under the choice of connection which Chern 50 atributes (below (10)) to

- André Weil,
*Géométrie différentielle des espaces fibres*, unpublished

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:

- Jean-Louis Koszul,
*Homologie et cohomologie des algebres de Lie*, Bull. Soc. Math. France vol. 78 (1950) pp. 65-127

Later, an independent proof of the universal topological “Chern-Weil”-construction $inv(\mathfrak{g}) \to H^\bullet(B G)$ is given in:

- Raoul Bott,
*On the Chern-Weil homomorphism and the continuous cohomology of Lie-groups*, Advances in Mathematics Volume 11, Issue 3, December 1973, Pages 289-303 (doi:10.1016/0001-8708(73)90012-1)

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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))

]]>Yet more ancient references, this time kindly dug out by Alan Hatcher.

]]>I pasted some historical comments and references (but still incomplete currently) provided by Jim Stasheff into Chern-Weil theory. More to come.

]]>tried to polish a bit the matrial at Chern-Weil theory.

(not that there is much, yet, but still)

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