Timeline for An example of a complex manifold without a finite open cover
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 4, 2012 at 20:33 | answer | added | Lucas Kaufmann | timeline score: 5 | |
| Jul 28, 2011 at 0:52 | vote | accept | Vamsi | ||
| Jul 27, 2011 at 18:49 | answer | added | Albuquerque | timeline score: 1 | |
| Jul 21, 2011 at 5:37 | comment | added | David Roberts♦ | If you don't put restrictions on the topology/geometry/etc of the open sets, then b) has a simple answer: every complex manifold has an open cover by one open set: the whole manifold :-P | |
| Jul 21, 2011 at 5:02 | answer | added | Finnur Larusson | timeline score: 26 | |
| Apr 8, 2011 at 17:27 | comment | added | Vamsi | If you have a good finite open cover, the betti numbers would be finite (I think) by a Mayer-Vietoris argument. | |
| Apr 5, 2011 at 12:47 | comment | added | Dmitri Panov | If there a simple example of a smooth manifold that does not satisfy b)? If you give such an example that might help to construct a complex manifold with this property. There are many surface of infinite genus, and the simplest one that I can imagine seem to satisfy b) even if the charts are assumed to be connected an contractible. | |
| Mar 21, 2011 at 8:15 | answer | added | Stefan Waldmann | timeline score: 2 | |
| Mar 20, 2011 at 21:56 | answer | added | Georges Elencwajg | timeline score: 3 | |
| Mar 20, 2011 at 18:58 | comment | added | Vamsi | Yeah I want it to be connected and second-countable. | |
| Mar 20, 2011 at 17:51 | comment | added | Ryan Budney | A simple example of (b) would be a disjoint union of countably-many copies of $\mathbb C$. Perhaps you want connected and/or other restrictions? | |
| Mar 20, 2011 at 17:46 | history | asked | Vamsi | CC BY-SA 2.5 |