Timeline for Finite CW complex with finite non-abelian fundamental group and higher homologies zero
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Aug 28, 2021 at 22:08 | vote | accept | piper1967 | ||
| S Aug 28, 2021 at 22:08 | vote | accept | piper1967 | ||
| S Aug 28, 2021 at 22:08 | |||||
| Aug 28, 2021 at 22:08 | vote | accept | piper1967 | ||
| S Aug 28, 2021 at 22:08 | |||||
| Aug 4, 2021 at 21:45 | history | became hot network question | |||
| Aug 4, 2021 at 16:08 | answer | added | mme | timeline score: 7 | |
| Aug 4, 2021 at 15:01 | answer | added | Jens Reinhold | timeline score: 16 | |
| Aug 4, 2021 at 14:32 | comment | added | Tim Campion | Note that if $G = \pi_1(X)$ is perfect, you are asking for a finite acyclic space $X$ with fundamental group $G$. There's a lot of literature about acyclic spaces which could be relevant. | |
| Aug 4, 2021 at 14:15 | comment | added | mme | In fact there is a 2-dimensional simplicial complex whose fundamental group is $2I$, the "binary icosahedral group", which is nonabelian and perfect and order 120, and whose homology groups $H_i$ are all zero for all $i \geq 1$. This can be constructed by identifying appropriate twists of antipodal faces on a dodecahedron (and triangulating each pentagon), but to the modern eye the fastest description is probably "This is the punctured Poincare homology sphere". | |
| Aug 4, 2021 at 14:15 | review | Close votes | |||
| Aug 6, 2021 at 9:55 | |||||
| Aug 4, 2021 at 14:02 | comment | added | piper1967 | I edited the question. I meant finite non-abelian group in $\pi_1.$ | |
| Aug 4, 2021 at 14:01 | history | edited | piper1967 | CC BY-SA 4.0 |
edited title
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| Aug 4, 2021 at 14:00 | answer | added | Johannes Hahn | timeline score: 5 | |
| Aug 4, 2021 at 13:54 | comment | added | Tim Campion | Is there anything wrong with a bouquet of circles? | |
| Aug 4, 2021 at 13:45 | review | First posts | |||
| Aug 4, 2021 at 14:15 | |||||
| Aug 4, 2021 at 13:44 | history | asked | piper1967 | CC BY-SA 4.0 |