Timeline for Classifying spaces of topological groups that are not well-pointed
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 11, 2012 at 14:30 | answer | added | Peter May | timeline score: 3 | |
| Aug 10, 2012 at 22:43 | comment | added | Dan Ramras | Oscar, thanks. I deleted my comment, since yours addresses the relationship with the infinite join correctly... | |
| Aug 10, 2012 at 22:15 | comment | added | Oscar Randal-Williams | @Dan: The infinite join of copies of $G$, $\mathcal{B} G$, has a map down to the infinite join of copies of $*$, which is $\Delta^\infty$. It is different from $BG$, with either the fat or thin realisation (this is all in Segal's paper). | |
| Aug 10, 2012 at 15:09 | comment | added | André Henriques | The example I would try to work out in detail is the compact group given by an infinite product of copies of $\mathbb Z/2$. You should also keep in mind that there are two possible ways of interpreting $B_\bullet(pt,G,pt)$: one using the usual geometric realization, and one using the fat geometric realization. | |
| Aug 10, 2012 at 13:15 | comment | added | Mark Grant | Looking at Segal's "Classifying spaces and spectral sequences" (section 3) it seems that the bundle map you describe is not locally trivial in general. But perhaps it is when $G$ is compactly-generated weak Hausdorff (a standing assumption in Rudyak's book)? | |
| Aug 10, 2012 at 13:09 | comment | added | some guy on the street | Not that I know how to answer in that case, but just to be clear, by "topological group", does it mean strict group? | |
| Aug 10, 2012 at 12:44 | comment | added | Mark Grant | I guess you mean theorem 1.65 in chapter IV? | |
| Aug 10, 2012 at 12:21 | history | asked | Ulrich Pennig | CC BY-SA 3.0 |