Timeline for space of closed subgroups of profinite group
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 19, 2017 at 12:22 | answer | added | ChanaG | timeline score: 2 | |
| Jan 12, 2017 at 10:14 | answer | added | user05811 | timeline score: 3 | |
| Jan 11, 2017 at 20:05 | comment | added | YCor | I think that for $G$ compact $Sub(G)/\sim$ is always totally disconnected (this is trivial if $G$ is profinite but otherwise $Sub(G)$ need not be totally disconnected, e.g., for $G=SO(3)$). | |
| Jan 11, 2017 at 15:44 | comment | added | YCor | For the bare definition, the topology makes sense on the set of all closed subsets: when the compact group is metrizable and endowed with a compatible metric, it is just given by the Hausdorff distance between nonempty closed subsets. This is a compact set, and the set of closed subgroup is a compact subsets therein. In the totally disconnected case, it's naturally a profinite set. | |
| Jan 11, 2017 at 15:42 | comment | added | YCor | There are many references, usually called "Chabauty topology" (for an arbitrary locally compact group); actually Chabauty introduced it in the 50s to compactify the space of lattices in a Euclidean space. This topology appeared at many places, including Bourbaki. A number of papers appeared in Russian journals in the 80s about spaces of subgroups. In the last 10 years it became again fashionable. | |
| Jan 11, 2017 at 15:30 | history | asked | PrimeRibeyeDeal | CC BY-SA 3.0 |