# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 8th 2011

added to Chern-Weil homomorphism the description of the construction of the refined CW homomorphism by differential functions built using the universal connection as described by Hopkins-Singer.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeMar 28th 2012

The letter $P$ is used in the first paragraph both for the invariant polynomial and for the total space of the principal bundle. I did not change it as I do not know which one to change to stay in accordance with other entries on the topic. Urs ?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMar 28th 2012

Thanks. I have changed the invariant polynomial notation to “$\langle -\rangle$”.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeDec 15th 2018
• (edited Dec 15th 2018)

Thanks!

I have moved the section to before the “refined” version, renamed to “The plain Chern-Weil homomorphism” (okay?) and instead added pointer to the actual reference Kobayashi-Nomizu 63

1. Thanks Urs. It looks good for me.
• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeDec 15th 2018
• (edited Dec 15th 2018)

All right.

L Probably it’s the hyphen bug at work, which keeps haunting the nLab.

• CommentRowNumber7.
• CommentAuthorDavid_Corfield
• CommentTimeDec 15th 2018

Isn’t it that the category of the other thread is ’nLab’ rather than ’Latest Changes’ here?

2. As mentioned by David, the category of thread is nLab there.
• CommentRowNumber9.
• CommentAuthorRichard Williamson
• CommentTimeDec 15th 2018
• (edited Dec 15th 2018)

Yes, David C is correct. Let me know if the two threads should be merged. I am not aware of any present hyphen bug :-).

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeDec 15th 2018

I think there is still a problem with some links on the nLab not working, because hyphens that look the same have different character encodings. I stopped reporting that long ago, but if you have the energy, I will drop a message next time I encounter it.

3. Ah, yes, please do. We have a similar issue registered on the Technical TODO list (nlabmeta). I think people do it unintentionally, but if anyone is deliberately making a choice, I’d suggest to keep it simple and use the usual Ascii hyphen rather a unicode em or en dash :-).

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeDec 15th 2018

I think the problem comes not so much from people making choices, but from some non-trivial transformation happening in the process of a) typing a hyphen into the source code, b) it being rendered (and maybe differently in bulk text and headlines?) and this rendered output c) being copy-and pasted into the next source.

But I’ll check.

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeAug 25th 2020
• (edited Aug 25th 2020)

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeAug 26th 2020

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeAug 28th 2020

turns out that Weil’s unpublished note is available in his collected works, have added the pointers:

• André Weil, Géométrie différentielle des espaces fibres, unpublished, item [1949e] in: André Weil Oeuvres Scientifiques / Collected Papers, vol. 1 (1926-1951), 422-436, Springer 2009 (ISBN:978-3-662-45256-1)
• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeAug 28th 2020

I finally realized that Cartan’s article exists in two different versions. Have now made the citation read as follows:

• Henri Cartan, Section 7 of: _Cohomologie réelle d’un espace fibré principal différentiable. I : notions d’algèbre différentielle, algèbre de Weil d’un groupe de Lie _, Séminaire Henri Cartan, Volume 2 (1949-1950), Talk no. 19, 10 p. (numdam:SHC_1949-1950__2__A18_0)

\linebreak

Henri Cartan, Section 7 of: Notions d’algèbre différentielle; applications aux groupes de Lie et aux variétés où opère un groupe de Lie, in: Centre Belge de Recherches Mathématiques, Colloque de Topologie (Espaces Fibrés) Tenu à Bruxelles du 5 au 8 juin 1950, Geroges Thon 1951 (GoogleBooks)

\linebreak

(These two articles have the same content, with the same section outline, but not the same wording. The first one is a tad more detailed.)

• CommentRowNumber17.
• CommentAuthorUrs
• CommentTimeAug 28th 2020
• (edited Aug 28th 2020)

Funny how it goes:

Cartan gives prominently placed seminars about the idea, and publishes it in an on-topic book collection.

Three months later Chern gives a talk with quick reference to an unpublished and unavailable note by Weil, and henceforth Cartan’s idea is known as “Chern-Weil theory”. :-)

• CommentRowNumber18.
• CommentAuthorUrs
• CommentTimeAug 28th 2020

added pointer to Section 2 of

• CommentRowNumber19.
• CommentAuthorUrs
• CommentTimeAug 28th 2020

Have added more references, such as to the universal connections that Chern had been appealing to. Also pointers to these further reviews: