Timeline for When is equivariant cohomology generated by equivariant Euler classes?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 26, 2014 at 20:20 | comment | added | Peter Crooks | I had the impression that it was the classes of the fixed point sets, but it is looking increasingly likely that I am not remembering things correctly. I will definitely ask for clarification. | |
| Jan 26, 2014 at 20:03 | comment | added | Allen Knutson | Are you sure it was the classes of the actual fixed point sets, rather than the closures of their unstable manifolds? | |
| Jan 25, 2014 at 9:52 | comment | added | Peter Crooks | The only explicit example that occurs to me is the usual action of $\mathbb{C}^*$ on $\mathbb{P}^1$. I ask because I recall having heard a speaker suggest there was a large class of examples in equivariant symplectic geometry in which this occurs. I will try to ask the speaker for clarification, and possibly the examples themselves. | |
| Jan 25, 2014 at 9:08 | comment | added | Allen Knutson | I'm of the opinion that Dave's necessary condition above shows that the situation asked for is pretty weird. Did you have any examples to motivate it? | |
| Jan 24, 2014 at 19:25 | comment | added | Dave Anderson | Even requiring all $F_i$ to have codimension $1$ is not sufficient, though: take a positive-genus curve $C$ and consider ${\Bbb P}^1 \times C$ with the standard ${\Bbb C}^*$ action on the first factor. | |
| Jan 24, 2014 at 19:16 | comment | added | Dave Anderson | A simple necessary condition is for at least one component $F_i$ to have (complex) codimension one, since $H_T^2(X)$ is nonzero. This rules out lots of the common examples, e.g., ${\Bbb P}^n$ with the standard $n$-dimensional torus action. (On the other hand, if you invert those Euler classes, both sides become isomorphic.) | |
| Jan 24, 2014 at 16:53 | history | asked | Peter Crooks | CC BY-SA 3.0 |