Timeline for Approximate classifying space by boundaryless manifolds?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 27 at 1:45 | comment | added | Michael Albanese | When $G$ is discrete, $BG$ is a $K(G, 1)$. Do you know if there is a model for $K(G, n)$ which is a colimit of closed manifolds? There is such a model for $K(\mathbb{Z}, 2)$ for example (namely $\mathbb{CP}^{\infty}$). | |
| Apr 1 at 22:16 | comment | added | mme | The earliest example I see exploiting the embedding $G \hookrightarrow U(k)$ to give topological information about $BG$ is Venkov, 1959, which uses this and the Leray--Serre spectral sequence to argue that $H^*(BG)$ is finitely generated. This observation is mentioned in Dieudonne's history of topology (the final paragraph of 3.2.F), but as a part of the mathematical exposition and not a historical comment. It seems quite plausible from context it could have appeared earlier in foundational work of Whitney, but I'm not sure. | |
| Apr 1 at 19:46 | vote | accept | 0207 | ||
| Apr 1 at 17:48 | history | answered | mme | CC BY-SA 4.0 |