Timeline for Universal cover of finetely connected surface with boundary
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 24, 2021 at 10:13 | comment | added | Greg Friedman | If $g=0$ then you're cutting things out of the sphere, which is basically the same picture with a finite number of holes, so that case is simpler. | |
| May 24, 2021 at 10:10 | comment | added | Greg Friedman | So up to homotopy this is something like the universal cover an infinite wedge of circles, independent of $r$ and $k$ so long a one of them is positive. | |
| May 24, 2021 at 10:07 | comment | added | Greg Friedman | I think you can see this, to the extent that it's seeable, by going to the universal cover in steps. First start with the compact orientable surface and take its universal cover. Focusing on genus $g\geq 1$, that gives you a plane that you can think of as partitioned into fundamental domains that each map to a dense set of the surface. Now, up to some isotopies, poking holes and cutting out disks can be done in the interior of the fundamental domain, so in the covering space you get a countable number of holes and countable number of removed disks. So now take the universal cover of that. | |
| May 23, 2021 at 23:11 | history | asked | Eduardo Longa | CC BY-SA 4.0 |