Timeline for Why "Classification" of 4 manifolds is NOT possible?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2017 at 22:56 | comment | added | Joshua Grochow | I had trouble finding an actual copy of the Papakyriakopoulos paper, but I did find this later paper [Whittlesey '58] with a proof of the same result, so I thought others might find the link useful: jstor.org/stable/2033313. I'd be grateful for a digital version of the Papakyriakopoulos paper. | |
| Aug 31, 2011 at 20:59 | vote | accept | user16750 | ||
| Aug 27, 2011 at 22:25 | comment | added | Autumn Kent | Something that bugs me whenever this is discussed: Papakyriakopoulos solved the homeomorphism problem for 2-complexes, which have all finitely presented groups among their fundamental groups. So you can tell two presentation 2-complexes apart (up to homeomorphism), even though you can't tell if their fundamental groups are isomorphic. So Markov's theorem about there being no solution to the homeomorphism problem for 4-manifolds is a little more subtle than everyone lets on. | |
| Aug 27, 2011 at 3:51 | history | answered | Allen Knutson | CC BY-SA 3.0 |