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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2020

    starting something

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2020

    added this pointer:

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 11th 2020

    Added pointer to:

    diff, v5, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 11th 2020

    added this pointer:

    diff, v5, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 9th 2021

    added point to

    • 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)

    diff, v7, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMar 9th 2021

    added pointer to:

    diff, v7, current

    • 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…

    diff, v7, current

    • 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 GG the author constructs an equivariant Chern homomorphism from K GK_G to H ev(,R G)H^{ev}( ,R_G) which is a rational isomorphism for compact GG-CW-complexes XX, and uses it to express K G(X)QK_G(X)\otimes \mathbf{Q} in terms of all K(X H)K(X^H) with HH a cyclic subgroup of GG. The basic tool is the notion of a “split coefficient system” and its properties; this is a GG-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
    • CommentTimeJan 31st 2022

    Thanks!!

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