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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 4th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something <a href="https://ncatlab.org/nlab/revision/equivariant+Chern+character/1">v1</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Chern+character">current</a>

   starting something

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 4th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this pointer: * [[Ulrich Bunke]], Section 3.1 in: _Orbifold index and equivariant K-homology_, Math. Ann. 339, 175–194 (2007) ([arXiv:math/0701768](https://arxiv.org/abs/math/0701768), [doi:10.1007/s00208-007-0111-5](https://doi.org/10.1007/s00208-007-0111-5)) <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Chern+character/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Chern+character/4">v4</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Chern+character">current</a>

   added this pointer:

   • Ulrich Bunke, Section 3.1 in: Orbifold index and equivariant K-homology, Math. Ann. 339, 175–194 (2007) (arXiv:math/0701768, doi:10.1007/s00208-007-0111-5)

   diff, v4, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 11th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded pointer to: * [[Ulrich Bunke]], [[Markus Spitzweck]], [[Thomas Schick]], _Inertia and delocalized twisted cohomology_, Homotopy, Homology and Applications, vol 10(1), pp 129-180 (2008) ([arXiv:math/0609576](https://arxiv.org/abs/math/0609576)) <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Chern+character/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Chern+character/5">v5</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Chern+character">current</a>

   Added pointer to:

   • Ulrich Bunke, Markus Spitzweck, Thomas Schick, Inertia and delocalized twisted cohomology, Homotopy, Homology and Applications, vol 10(1), pp 129-180 (2008) (arXiv:math/0609576)

   diff, v5, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeOct 11th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this pointer: * [[Alain Connes]], [[Paul Baum]], _Chern character for discrete groups_, A Fête of Topology, Papers Dedicated to Itiro Tamura 1988, Pages 163-232 ([doi:10.1016/B978-0-12-480440-1.50015-0](https://doi.org/10.1016/B978-0-12-480440-1.50015-0)) <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Chern+character/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Chern+character/5">v5</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Chern+character">current</a>

   added this pointer:

   • Alain Connes, Paul Baum, Chern character for discrete groups, A Fête of Topology, Papers Dedicated to Itiro Tamura 1988, Pages 163-232 (doi:10.1016/B978-0-12-480440-1.50015-0)

   diff, v5, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 9th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded 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) <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Chern+character/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Chern+character/7">v7</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Chern+character">current</a>

   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

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMar 9th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Alejandro Adem]], [[Yongbin Ruan]], Section 5 of: _Twisted Orbifold K-Theory_, Commun. Math. Phys. 237 (2003) 533-556 ([arXiv:math/0107168](https://arxiv.org/abs/math/0107168)) <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Chern+character/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Chern+character/7">v7</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Chern+character">current</a>

   added pointer to:

   • Alejandro Adem, Yongbin Ruan, Section 5 of: Twisted Orbifold K-Theory, Commun. Math. Phys. 237 (2003) 533-556 (arXiv:math/0107168)

   diff, v7, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeMar 9th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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... <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Chern+character/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Chern+character/7">v7</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Chern+character">current</a>

   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

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJan 28th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexMight 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. ?

   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.

   ?

9. • CommentRowNumber9.
   • CommentAuthorDavidRoberts
   • CommentTimeJan 29th 2022
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexWow, 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.

   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.

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJan 30th 2022
    • PermaLink
    Author: Urs
    Format: MarkdownItexThanks 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](https://ncatlab.org/schreiber/files/MislinValette_p22-24.pdf#page=1)) that the ideas on splitting of the rationalized representation ring (discussed and referenced [here](https://nforum.ncatlab.org/discussion/13784/splitting-of-rationalized-representation-ring/?Focus=97448#Comment_97448)) 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.

    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.

11. • CommentRowNumber11.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJan 31st 2022
    • PermaLink
    Author: Dmitri Pavlov
    Format: MarkdownItexRe #10: The PDF file is available here: <https://dmitripavlov.org/scans/słomińska.pdf>.

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

12. • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeFeb 1st 2022
    • PermaLink
    Author: Urs
    Format: MarkdownItexThanks!!

    Thanks!!