Timeline for Compact closed aspherical manifolds with vanishing second homology in all the covering spaces
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| S Mar 30, 2023 at 10:21 | history | bounty ended | Zhenhua Liu | ||
| S Mar 30, 2023 at 10:21 | history | notice removed | Zhenhua Liu | ||
| Mar 28, 2023 at 18:52 | vote | accept | Zhenhua Liu | ||
| Mar 28, 2023 at 17:32 | answer | added | Ian Agol | timeline score: 4 | |
| Mar 24, 2023 at 13:06 | comment | added | HJRW | @MoisheKohan: Of course, thanks for resolving my worries! | |
| Mar 24, 2023 at 2:25 | comment | added | Moishe Kohan | It will be a wasted bounty. | |
| Mar 24, 2023 at 0:39 | comment | added | Moishe Kohan | @HJRW: It contains $BS(1,4)$, thus, is not a problem. | |
| S Mar 23, 2023 at 21:36 | history | bounty started | Zhenhua Liu | ||
| S Mar 23, 2023 at 21:36 | history | notice added | Zhenhua Liu | Draw attention | |
| Mar 22, 2023 at 18:22 | comment | added | HJRW | @IanAgol: Ah, OK. (There’s a typo in that part of the question, so it’s somewhat unclear.) I’m still a little worried about BS(1,2)… | |
| Mar 22, 2023 at 17:35 | comment | added | Ian Agol | @hjrw: the question asks for trivial homology with finite coefficients as well. | |
| Mar 22, 2023 at 17:08 | history | edited | Moishe Kohan | CC BY-SA 4.0 |
added 5 characters in body
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| Mar 22, 2023 at 17:08 | comment | added | Moishe Kohan | Please, check the correctness of my edit. | |
| Mar 22, 2023 at 11:09 | history | edited | Zhenhua Liu | CC BY-SA 4.0 |
Fixing typo
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| Mar 22, 2023 at 7:08 | comment | added | HJRW | @IanAgol: which subgroup do you have in mind for the solvable Baumslag—Solitar groups? The finite-sheeted covers have trivial $H_2$, as does the infinite cyclic cover. (I mean with $\mathbb{Z}$ coefficients, of course.) | |
| Mar 22, 2023 at 6:11 | comment | added | Fernando Muro | What’s the condition for $v\geq 2$? | |
| Mar 22, 2023 at 0:03 | comment | added | Moishe Kohan | I am quite sure that no such examples are known. | |
| Mar 21, 2023 at 21:29 | comment | added | Igor Belegradek | A weak version of what you ask for: There is a closed aspherical $16$-dimensional manifold $M$ such that every finitely-sheeted coverings $\bar M$ of $M$ has finite $H_i(\bar M)$ for $i=1,2,3$. Here $M$ is any closed Cayley hyperbolic manifold, see section 8 in "Nonarithmetic Superrigid Groups: Counterexamples to Platonov's Conjecture" by Bass and Lubotzky, arxiv.org/pdf/math/0005302.pdf. | |
| Mar 21, 2023 at 21:05 | comment | added | Ian Agol | If one had a closed aspherical manifold with this property, then its fundamental group could not contain a Baumslag-Solitar subgroup; such a group has a subgroup with non-trivial $H_2$. Examples of groups that do not contain Baumslag-Solitar subgroups are hyperbolic groups. However, Gromov has conjectured that hyperbolic groups contain a surface subgroup, and hence would have a subgroup with non-trivial $H_2$ if that conjecture is true. Moreover, until recently a group of finite type which was non hyperbolic and contained no Baumslag-Solitar subgroup was not known.arxiv.org/abs/2105.14795 | |
| Mar 21, 2023 at 20:01 | history | asked | Zhenhua Liu | CC BY-SA 4.0 |