Timeline for Classification problem for non-compact manifolds
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
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| Jan 9, 2012 at 6:16 | answer | added | Matt Brin | timeline score: 7 | |
| Apr 13, 2010 at 16:03 | answer | added | Benoît Kloeckner | timeline score: 35 | |
| Jan 12, 2010 at 15:15 | history | edited | Dmitri Panov | CC BY-SA 2.5 |
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| Jan 12, 2010 at 9:27 | answer | added | Dmitri Panov | timeline score: 13 | |
| Jan 12, 2010 at 9:05 | comment | added | Dmitri Panov | I think, that the first 10 lines of Maillot's article give an answer to your quesiton. Here is a citation: "For open 3-manifolds, by contrast, there is not even a conjectural description of a general 3-manifold in terms of geometric ones". arxiv.org/PS_cache/arxiv/pdf/0802/0802.1438v2.pdf | |
| Jan 9, 2010 at 22:03 | answer | added | algori | timeline score: 17 | |
| Jan 9, 2010 at 21:04 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
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| Nov 16, 2009 at 5:44 | history | edited | Greg Kuperberg |
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| Nov 15, 2009 at 18:40 | answer | added | Jason DeVito - on hiatus | timeline score: 10 | |
| Nov 6, 2009 at 3:56 | comment | added | Ryan Budney | And you of course you can do things with manifolds by avoiding direct discussion of the fundamental group. The classification of 3-manifolds in essence says that 3-manifolds are classified by their fundamental groups modulo the issue of lens space summands. But that's not how the proof goes. Similarly, Rubinsteins 3-sphere recognition algorithm does not discuss the fundamental group, even though the 3-sphere is the only compact boundaryless 3-manifold with a trivial fundamental group. Presumably there could be an analogue of Rubinstein's algorithm for triangulated 4-manifolds. | |
| Nov 6, 2009 at 3:01 | comment | added | Ryan Budney | People don't stick to only simply-connected manifolds. 4-manifolds having amenable fundamental group is a popular class, for example. Basically, any class where some aspects of the fundamental group aren't out of control are okay. From the point of view of classification you want to restrict to a class of groups where the isomorphism problem is tractible. | |
| Nov 5, 2009 at 0:01 | answer | added | Ryan Budney | timeline score: 29 | |
| Nov 4, 2009 at 22:49 | answer | added | HJRW | timeline score: 12 | |
| Nov 4, 2009 at 22:49 | answer | added | Harrison Brown | timeline score: 3 | |
| Nov 4, 2009 at 22:33 | history | asked | Victoria Flat | CC BY-SA 2.5 |