Timeline for Representation viewpoint on Chern–Weil (cohomology computations done with rep theory?)
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 30, 2016 at 13:20 | comment | added | Allen Knutson | First prove, using the map $G/T \to G/N(T)$, that the space $G/N(T)$ has only even cohomology but $\chi=1$ hence trivial rational cohomology. Then use Leray-Hirsch on $EG/N(T) \to EG/G$ to show they have the same rational cohomology. Finally, use the Galois covering space $EG/T \to EG/N(T)$ to show $EG/N(T)$'s cohomology is the $W$-invariants in that of $EG/T$. | |
| Apr 30, 2016 at 10:35 | comment | added | Saal Hardali | Wow. This is a lot of content. Thanks! A few questions though: 1. Where can I find a neat proof of $H^{\bullet}(BG ; \mathbb{Q})=H^{\bullet}(BT;\mathbb{Q})^W$? 2.Is there somekind of map of stacks $[*/G] \to [T/W]$? 3.What about an "exponential" map $[\mathfrak{g}/G] \to [G/G]$? 4.Where can I read about all this stuff (algebraic topology computations mixd with rep theory)? Is there a single source? Maybe a collection of sources? | |
| Apr 30, 2016 at 10:28 | vote | accept | Saal Hardali | ||
| Apr 29, 2016 at 15:41 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |