Timeline for Cohomology ring of BG
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 20, 2012 at 20:40 | comment | added | Johannes Ebert | See mathoverflow.net/questions/61784/… | |
| Dec 20, 2012 at 20:40 | comment | added | Ralph | Craig, thanks for the clarification. | |
| Dec 20, 2012 at 20:30 | answer | added | Ralph | timeline score: 10 | |
| Dec 20, 2012 at 20:16 | comment | added | Paul Siegel | Ah, quite right - I should have specified that I was defining $H^*(X)$ to be the product of $H^n(X)$ over all $n$. This question came up as I was working through some computations with characteristic classes, and this is apparently a common convention in that context. | |
| Dec 20, 2012 at 20:15 | answer | added | Chris Gerig | timeline score: 1 | |
| Dec 20, 2012 at 20:04 | comment | added | Craig Westerland | The differences between the power series and polynomial rings in this case depend upon your choice to define $H^\ast(X)$ as either the product or sum over all $n$ of $H^n(X)$. | |
| Dec 20, 2012 at 20:03 | answer | added | Craig Westerland | timeline score: 6 | |
| Dec 20, 2012 at 19:55 | comment | added | Ralph | Paul, sorry, but I doubt that this is well-known. The cohomology of $BS^1$ is a polynomial ring in one variable. Also note that $H^\ast(\mathbb{C}P^n)=\mathbb{Z}[x]/(x^{n+1})$. | |
| Dec 20, 2012 at 19:39 | comment | added | Paul Siegel | I think so... for example, the classifying space of $S^1$ is $\mathbb{C}P^\infty$, and the cohomology of $\mathbb{C}P^\infty$ is well known to be the ring of formal power series in one variable. | |
| Dec 20, 2012 at 19:23 | comment | added | Ralph | Do you really mean power series $\mathbb{Q}[[x_1, \ldots, x_n]]$ ? | |
| Dec 20, 2012 at 19:12 | history | edited | Angelo | CC BY-SA 3.0 |
added 2 characters in body
|
| Dec 20, 2012 at 19:10 | history | asked | Paul Siegel | CC BY-SA 3.0 |