Timeline for On direct limit of Stiefel mainfold
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2013 at 0:38 | answer | added | Peter Michor | timeline score: 1 | |
| Jan 13, 2013 at 21:15 | comment | added | Fernando Muro | @Tom, if you mean locally trivial when you say "strong", then it holds under very general topological assumtions satisfied by this example, see eg ncatlab.org/nlab/show/principal+bundle | |
| Jan 13, 2013 at 16:43 | comment | added | Tom Goodwillie | I think that the OP is using "free" for a topological group action in a strong sense: not only is there no isotropy but the map to the orbit space is a (principal) bundle. I don't know how generally it is true that a $U(n)$-action with trivial isotropy groups is free in the strong sense, but in this case you can explicitly make trivializing open sets: just think of how you make charts in the (finite-dimensional) Grassmannians by looking at where a given set $n$ of the $k$ coordinates are nonzero. It still works with $k$ infinite. | |
| Jan 13, 2013 at 15:58 | comment | added | Fernando Muro | The limit is a union, ie a direct limit of injective maps. If a point had isotropy in the union then it would have isotropy in the first Stiefeld manifold it belongs to. | |
| Jan 13, 2013 at 15:44 | history | asked | Oscar1778 | CC BY-SA 3.0 |