Timeline for What is the easiest way to classify all possible smooth orientable closed 2-manifolds?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Apr 15, 2010 at 10:41 | answer | added | John Stillwell | timeline score: 6 | |
| Apr 15, 2010 at 6:20 | answer | added | Sebastian | timeline score: 2 | |
| Apr 14, 2010 at 17:06 | comment | added | Andy Putman | @Andrew L - All of these methods are constructive and visual; it just depends on how they are presented. In any case, if you like the combinatorial approaches, then I recommend you check out Conway's "ZIP proof", which is combinatorial but even more constructive and visual than the old-fashioned one. | |
| Apr 14, 2010 at 17:02 | comment | added | The Mathemagician | I like the good old fashioned combinatorial method of Rado.Yes,it's tedious,but it has the advantage of being constructive and highly visual. | |
| Apr 14, 2010 at 15:22 | comment | added | Deane Yang | @Andy: Thanks! The proof in Hirsch's book, Differential Topology, looks like what I want. | |
| Apr 14, 2010 at 15:21 | comment | added | Andy Putman | If you want to start with a smooth structure, then use Morse theory. It's easy -- all you have to check is that if you start with a (possibly disconnected) cpt orientable surface with bdry that's covered by the classification and attach a k-handle for k=0,1,2, then you get a surface covered by the classification (a Morse fcn gives a handle decomp of your mnfld). Adding a 0-handle is taking the disjoint union with a disc and adding a 2-handle is gluing a disc to a bdry cpt, so these cases are easy. For a 1-handle, once you draw the picture you'll see that there are 3 special cases to check. | |
| Apr 14, 2010 at 15:15 | answer | added | Tony Huynh | timeline score: 1 | |
| Apr 14, 2010 at 15:12 | history | edited | Deane Yang | CC BY-SA 2.5 |
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| Apr 14, 2010 at 14:57 | answer | added | Scott Carter | timeline score: 2 | |
| Apr 14, 2010 at 14:34 | comment | added | Andy Putman | I gave a list of various proofs in my answer to this question : mathoverflow.net/questions/20438/… | |
| Apr 14, 2010 at 14:26 | history | asked | Deane Yang | CC BY-SA 2.5 |