Timeline for Idempotent conjecture and (weak) connectivity of (a reasonable) dual group
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 20, 2023 at 17:22 | comment | added | Ali Taghavi | @BenjaminSteinberg yes that is true for abelian group. The complete proof is given in the post for discrete abelian. In fact the surjectivity of the assembly map implies the Kaplanski conjecture. Anyway I am interested in the mitivation part of this post too. | |
| Aug 20, 2023 at 16:02 | comment | added | Benjamin Steinberg | I believe the Kadison-Kaplansky conjecture is known for torsion-free abelian groups. It is true for any group for which Baum-Connes holds and that includes abelian groups I believe. | |
| Aug 20, 2023 at 13:27 | comment | added | Onur Oktay | For other examples, the inverse limits of compact connected Lie groups may be good candidates. Inverse limits of compact (resp. connected LC) groups are compact (resp. connected LC) groups, provided the connecting maps are surjective. The same is not always valid for path connectedness. p-adic solenoid is actually a representative example. | |
| Aug 20, 2023 at 10:34 | comment | added | მამუკა ჯიბლაძე | The $p$-adic solenoids, i. e. duals of $\mathbb Z[\frac1p]$, are not path connected | |
| Aug 20, 2023 at 10:25 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
added 229 characters in body
|
| Aug 20, 2023 at 10:10 | history | asked | Ali Taghavi | CC BY-SA 4.0 |