Timeline for Finite CW complex with finite non-abelian fundamental group and higher homologies zero
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 4, 2021 at 14:45 | comment | added | Z. M | And seemingly the higher homology groups of $K(G,1)$, i.e. group homology of $G$, are not trivial in general? | |
| Aug 4, 2021 at 14:27 | comment | added | piper1967 | I have edited my question. I meant for a finite non-abelian group in $\pi_1.$ | |
| Aug 4, 2021 at 14:22 | comment | added | Tim Campion | +1 I learned something from this! After the edit, I suppose it doesn't quite answer the question, since the OP wants $\pi_1(X)$ to be finite. As explained here, if $G$ has any torsion, then any $K(G,1)$ must have cells in arbitrarily large dimension, and so $K(G,1)$ is not finite. | |
| Aug 4, 2021 at 14:00 | history | answered | Johannes Hahn | CC BY-SA 4.0 |