Timeline for Pullbacks of classifying spaces
Current License: CC BY-SA 4.0
4 events
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| Nov 13, 2023 at 16:38 | comment | added | R. van Dobben de Bruyn | Ah, right, the realisations of the nerves do actually provide somewhat canonical models — e.g. for $\mathbf Z/2$ we get a space homeomorphic (rather than homotopy equivalent) to $\mathbf{RP}^\infty$, built from one simplex in each dimension (if I recall correctly). But for $\mathbf Z$, you get something much larger than the circle, so I never really think about this construction. I think your questions have now been addressed by Neil Strickland's answer. | |
| Nov 13, 2023 at 14:27 | comment | added | Tommaso Rossi | Just one question about the last few lines: let us agree that BG, BH, BH' are the topological spaces obtained by taking the geometric realization of the nerves N(G), N(H), N(H'). If $G\to H$ is surjective then the homotopy pullback of the span written on the top of your answer is the same of the ordinary pullback in the category of topological spaces. Is it right? | |
| Nov 13, 2023 at 14:11 | vote | accept | Tommaso Rossi | ||
| Nov 13, 2023 at 16:13 | |||||
| Nov 13, 2023 at 11:50 | history | answered | R. van Dobben de Bruyn | CC BY-SA 4.0 |