Timeline for Simple examples of equivariant homology and bordism
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 8, 2010 at 16:48 | comment | added | Mark Grant | If you wanted examples with non-trivial differentials, I think you would need all isotropy groups $G_x$ to be proper subgroups of $G$, but sadly I'm no expert. And of course in the previous comment I meant $E^2_{*,*}=H_*(G,H_*(X))$! | |
| Dec 8, 2010 at 16:43 | comment | added | Mark Grant | The only way I know of computing $H_*^G(X)=H_*(EG\times_G X)$ is by looking at the Leray-Serre spectral sequence of the Borel fibration $X\to EG\times_G X\to BG$. I think in both these cases all differentials are trivial, so it's just a case of computing $E^2_{*,*}=H^*(G, H^*(X))$. | |
| Dec 8, 2010 at 15:08 | comment | added | Daniel Moskovich | Okay... then how would the calculation go? | |
| Dec 8, 2010 at 14:23 | comment | added | Mark Grant | I mean to reflect in an equatorial plane (in say, the first factor). Then $\{equator\}\times S^n$ is left fixed. | |
| Dec 8, 2010 at 13:07 | comment | added | Johannes Hahn | If $\tau$ is the nontrivial group element, then $^\tau (x,x)=(x,x)$ for all $x\in S^n$ so the first action is not free. The second action is free. | |
| Dec 8, 2010 at 12:46 | comment | added | Daniel Moskovich | How is this action not free? | |
| Dec 8, 2010 at 9:38 | history | answered | Mark Grant | CC BY-SA 2.5 |