Timeline for Is there any "deep" relation between the localization theorem of equivariant cohomology and the localization theorem of equivariant K-theory
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7 events
| when toggle format | what | by | license | comment | |
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| Jun 5, 2023 at 0:36 | answer | added | Geordie Williamson | timeline score: 5 | |
| Mar 26, 2017 at 0:02 | answer | added | jdc | timeline score: 9 | |
| Sep 17, 2012 at 15:18 | comment | added | Zhaoting Wei | @Alexander Thank you for your comment! Yes I think Chern character map may be the answer and there are a lot of interesting theory on it (for example the paper by J. Block and E. Getzler "Equivariant cyclic homology and equivariant differential forms"). I will think more carefully about this. | |
| Sep 11, 2012 at 17:55 | comment | added | Alexander Woo | I'm still hoping someone who understands this better than me answers this, but... Yes - there is (at least in some cases) a "Chern map" taking (equivariant) vector bundles to their (equivariant) Chern classes, and this should be the relation you are looking for. | |
| Sep 11, 2012 at 5:46 | comment | added | Zhaoting Wei | Thank you for your comments Damian! Yes, as far as I know the localization theorem is true essentially for compact abelian Lie groups. | |
| Sep 11, 2012 at 5:11 | comment | added | Damian Rössler | The localization theorem for equivariant K-theory is valid even when $G$ is a finite group. On the other hand, I think (correct me if I am wrong) that the localisation theorem for equivariant cohomology needs $G$ to have positive dimension to have a non-trivial content. This suggests that there is a conceptual difference between them. | |
| Sep 10, 2012 at 16:22 | history | asked | Zhaoting Wei | CC BY-SA 3.0 |