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

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 9th 2010

stub for Cartan calculus

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeJul 9th 2010

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJul 9th 2010

Thanks, I was thinking of that, too. We should eventually have a separate entry on the Cartan model for equiv-cohomology…

• CommentRowNumber4.
• CommentAuthorKevin Lin
• CommentTimeJul 20th 2010
• (edited Jul 20th 2010)
To be added (by me later, or by someone else sooner): Cartan calculus for polyvector fields and Schouten-Nijenhuis bracket?

And here is a good reference for Cartan equivariant cohomology (as well as for other approaches).

I noticed that the equivariant cohomology page doesn't yet have anything at all about the Cartan approach.
• CommentRowNumber5.
• CommentAuthorzskoda
• CommentTimeJul 20th 2010

Cartan’s model for equivariant cohomology is limited to rather special spaces, like differentiable manifolds, no ? On the other hand, equivariant cohomology is studied for more general spaces and under more general topological groups.

• CommentRowNumber6.
• CommentAuthorKevin Lin
• CommentTimeJul 20th 2010
Correct. But I don't consider manifolds to be a "limited" class of spaces...
• CommentRowNumber7.
• CommentAuthorzskoda
• CommentTimeJul 20th 2010

Come on, locally compact groups are so important (those beyond Lie groups). Even if you consider differentiable manifolds, the group variable is often so much more general.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJul 20th 2010

Not sure what the issue is. Certainly Cartan’s model for equivariant cohomology deserves to be discussed or at least linked at the entry on equivariant cohomology.

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTimeJul 20th 2010
• (edited Jul 20th 2010)

Surely it has to be a section. I was asking for it a cuple of weeks ago. But Kevin’s complaint

I noticed that the equivariant cohomology page doesn’t yet have anything at all about the Cartan approach.

has an appropriate answer: we preferred to center the entry about the general approach. Special features are for special sections or even separate entries. Kevin answers that manifolds are general enough. I still disagree.

I would like to see also connection to the equivariant localization formulas. Very important in my nlab plans and need exactly the Cartan model for many aspects.

• CommentRowNumber10.
• CommentAuthorKevin Lin
• CommentTimeJul 20th 2010
• (edited Jul 20th 2010)
OK. I understand. It's of course fine with me to put the bulk of the Cartan model in a separate entry. But we agree that it deserves a few sentences at least in the equivariant cohomology page.
• CommentRowNumber11.
• CommentAuthorzskoda
• CommentTimeJul 20th 2010

It deserves a large section at least…

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeOct 30th 2020

Removed the reference to Henri Cartan (there is still a pointer to the Cartan model, so no info is lost, but the impression avoided that Cartan calculus is named after Henri Cartan). What’s an actual reference to a publication by Élie Cartan that could go here?