Timeline for Dimension of classifying space of a group
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 12, 2020 at 22:33 | vote | accept | lab | ||
| Oct 9, 2020 at 19:29 | comment | added | YCor | A variant in which $N$ is finitely generated: write the Baumslag-Solitar group as $G=\langle t,x\mid txt^{-1}=x^n\rangle$, with $n\ge 2$. Then in $G^2$, the subgroup $N$ generated by $\{(t,t^{-1}),(x,1),(1,x)\}$ is finitely generated, and normal. Then $G^2$ admits a 4-dimensional finite classifying space. But $N$ is not finitely presented so doesn't admit any finite classifying space. (Nevertheless I'm not claiming that $N$ has no 3-dimensional classifying space.) | |
| Oct 9, 2020 at 18:42 | history | answered | Denis T | CC BY-SA 4.0 |