Timeline for Is there a finitely presented group with infinite homology over $\mathbb{Q}$?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2020 at 17:43 | answer | added | IJL | timeline score: 6 | |
| S Aug 7, 2014 at 14:36 | history | suggested | Adam Przeździecki | CC BY-SA 3.0 |
Corrected along the comments of Alex Suciu and YCor.
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| Aug 7, 2014 at 14:15 | review | Suggested edits | |||
| S Aug 7, 2014 at 14:36 | |||||
| Aug 7, 2014 at 9:54 | comment | added | YCor | @Dmitry: you should edit the second sentence of your question according to Alex' comments. | |
| Aug 7, 2014 at 8:27 | comment | added | Alex Suciu | Yes, $H_2$ of an fp group is finitely generated. But, say, $H_3$ needs not be finitely generated. The first such example was given by John Stallings, in a seminal paper, titled, sure enough, A finitely presented group whose 3-dimensional integral homology is not finitely generated, see here. | |
| Aug 7, 2014 at 8:07 | comment | added | Dmitry Vaintrob | @Alex: I thought any group homology of a finitely presented group is finite-dimensional. Are there examples where $H_2$ isn't? And yes, "infinite" means infinite-dimensional | |
| Aug 7, 2014 at 8:04 | vote | accept | Dmitry Vaintrob | ||
| Aug 7, 2014 at 5:09 | answer | added | HJRW | timeline score: 18 | |
| Aug 7, 2014 at 4:26 | comment | added | Alex Suciu | Also, "infinite homology" means "infinite-dimensional homology" (as $\mathbb{Q}$-vector space), right? | |
| Aug 7, 2014 at 4:24 | comment | added | Alex Suciu | Just to make sure: the assertion that $H_i(G,\mathbb{Q})$ is finite-dimensional (for all $i>2$) is an assumption, yes? | |
| Aug 7, 2014 at 3:54 | history | asked | Dmitry Vaintrob | CC BY-SA 3.0 |