Timeline for An obstruction theory for promoting homotopy equivalences that are equivariant maps to equivariant homotopy equivalences?
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2010 at 3:37 | comment | added | Ben Wieland | Smith theory is about finite dimensional spaces, so you are in trouble. If $V$ is an infinite dimensional complex Frechet space, it has a natural $U(1)$-action, and $V-\{0\}\to V$ is an equivariant map that is an equivalence on total spaces, though the fixed sets are empty on the left and a point on the right. Maybe you can use some other finiteness assumptions, like control at infinity or finite codimension of the fixed sets, but this is not an off-the-shelf situation. | |
| Jun 29, 2010 at 3:00 | comment | added | Ryan Budney | Yes, I'm in the situation you describe in your 2nd paragraph. My space is a Frechet manifold with an action of $O(n)$ -- the simplest non-trivial case that I care about the group is $O(2)$. But the fixed point sets there's little technology out there that will help to describe their homotopy-type. | |
| Jun 29, 2010 at 2:17 | history | answered | Ben Wieland | CC BY-SA 2.5 |