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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJun 15th 2020

I have removed the bulk of the Idea section that I had written, starting way back when the entry was created in 2013.

I kept the other material that Mike (Shulman) had written.

I see now that mine was really besides the point.

Now that I finally understand this topic more deeply, maybe I find time to write a better explanation of what’s really going on.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeOct 16th 2021

• CommentRowNumber3.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 22nd 2022
• (edited May 22nd 2022)
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMay 22nd 2022

Thanks for the pointer.

Not sure what to make of this, the question seems to be specifically about the proper equivariant enhancement of the $S^1$-equivariance involved in the Witten genus, for which the section here at equivariant elliptic cohomology may be still the state of the art. But the OP says he has seen that page already.

One could say much more about proper equivariance in the discussion of D-brane charge and of topological phases of matter, where its crucial and fairly well understood, as indicted in our respective entries here and here. But I sense that this is not the reply that the OP wishes to see.

• CommentRowNumber5.
• CommentAuthornilesjohnson
• CommentTimeNov 26th 2022

just a typo fix ’tha’ -> ’that’

• CommentRowNumber6.
• CommentAuthornilesjohnson
• CommentTimeNov 26th 2022

another typo: ’suitble’ -> ’suitable’