Timeline for Properties of the class of topological spaces possessing a CW-structure
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2010 at 16:16 | comment | added | Igor Belegradek | There are different uses for the phrase "properly discontinuous G-action" but if you take the definition that "for any compact subset K only finitely many images of K intersect itself", then the above counterexample disappears. Under this definition, if G acts freely and properly discontinuously on a manifold X, then the quotient X/G is a (Hausdorff) manifold and the projection is a covering map. | |
| Jan 13, 2010 at 7:06 | vote | accept | Hanno | ||
| Jan 13, 2010 at 4:57 | comment | added | algori | Pete -- thanks for the reference! Honestly, I can't see any direct analogies with algebraic geometry, only some fairly vague ones, when the quotient turns out to be worse than expected (e.g an algebraic space instead of a scheme etc). One of the problems is that I don't see how to translate "properly discontinuous" into algebraic/categorical language. | |
| Jan 13, 2010 at 3:18 | comment | added | Pete L. Clark | This example can be found on wikipedia: en.wikipedia.org/wiki/Covering_space. (That's a good thing; I just wanted to point it out.) It's interesting -- the fact that the quotient by a free, properly discontinuous group action can lose the Hausdorff property is something I had never thought of before. Does this phenomenon show up naturally in algebraic or analytic geometry? | |
| Jan 13, 2010 at 1:02 | history | answered | algori | CC BY-SA 2.5 |