Timeline for Fundamental groups of noncompact surfaces
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2010 at 18:06 | comment | added | Andy Putman | @Ilya - that is the trivial case! There are a whole zoo of non-compact surfaces that are nowhere close to these examples. For instance, take a compact surface and remove a cantor set. I want arguments that handle those cases as well. | |
| Mar 17, 2010 at 17:37 | comment | added | Ilya Grigoriev | @Andy: This doesn't seem to be so hard if we can assume that the surface is a compact triangulated surface with some points removed. This is the same as removing the interiors of a few triangles. Then, whenever a see an edge that bounds a triangle on only one side, we remove both the edge and the interior of that triangle. This is a deform. retraction. The only way that this process can stop is when there are no filled-in triangles (assuming the surface was connected), so we have something 1-dimensional left. Did I miss something? Or do we need some generalization of this in your case? | |
| Mar 17, 2010 at 12:07 | comment | added | Igor Belegradek | Andy, this fact was mentioned in Brown's book "Cohomology of groups" in the proof of Proposition 8.1 (Chapter 8, Section 8). Brown does not give a reference. I do not know how the proof goes, and also would be interested in a reference. | |
| Mar 17, 2010 at 3:19 | comment | added | Andy Putman | Do you (or anyone else) know a reference for this "basic fact in PL-topology". I just skimmed through Rourke-Sanderson and didn't find it. | |
| Mar 17, 2010 at 3:15 | history | answered | Igor Belegradek | CC BY-SA 2.5 |