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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeOct 4th 2020

starting something

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeOct 4th 2020

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeOct 11th 2020

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeOct 11th 2020

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMar 9th 2021

• J. Słomińska, Equivariant Chern homomorphism, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys, Vol. 24 (1976), 909-913.

(the original reference(?), though I haven’t yet actually seen it)

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMar 9th 2021

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMar 9th 2021

I have !include-ed the table incarnations of rational equivariant topological K-theory – table.

This reminds me that rational equivariant K-theory should be a page on its own…

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJan 28th 2022

Might anyone have an electronic copy of

• Jolanta Słomińska, On the Equivariant Chern homomorphism, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys, Vol. 24 (1976), 909-913.

?

• CommentRowNumber9.
• CommentAuthorDavidRoberts
• CommentTimeJan 29th 2022

Wow, that journal seems to have missed the digitisation boat. That volume is on Google books, but with no preview available (I can see a few lines of the start of the article when searching inside, but nothing useful). For reference, here’s the complete MathSciNet review:

For any finite group $G$ the author constructs an equivariant Chern homomorphism from $K_G$ to $H^{ev}( ,R_G)$ which is a rational isomorphism for compact $G$-CW-complexes $X$, and uses it to express $K_G(X)\otimes \mathbf{Q}$ in terms of all $K(X^H)$ with $H$ a cyclic subgroup of $G$. The basic tool is the notion of a “split coefficient system” and its properties; this is a $G$-coefficient system in G. E. Bredon’s sense [Equivariant cohomology theories, Lecture Notes in Math., Vol. 34, Springer, Berlin, 1967; MR0214062] admitting suitable transfer maps.

The zbmath one is similarly brief.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeJan 30th 2022

Thanks for double-checking. Maybe I should walk into an actual library, for a change.

I don’t expect to find anything in Słomińska’s article that I wouldn’t essentially have seen reproduced elsewhere; but Mislin 2003 writes (p. 22) that the ideas on splitting of the rationalized representation ring (discussed and referenced here) due to Lueck & Oliver 1998 “have their root in Słomińska’s paper”. Since that splitting is a somewhat subtle business, I grew interested in seeing what Słomińska actually wrote about it.

• CommentRowNumber11.
• CommentAuthorDmitri Pavlov
• CommentTimeJan 31st 2022

Re #10: The PDF file is available here: https://dmitripavlov.org/scans/słomińska.pdf.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeFeb 1st 2022

Thanks!!