Timeline for Is the list of "known" 3D compact manifolds complete?
Current License: CC BY-SA 3.0
7 events
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| Nov 3, 2013 at 16:05 | comment | added | Misha | Igor, in the case of manifolds with boundary, one can use the algorithm for recognition of Haken manifolds instead. | |
| Nov 3, 2013 at 15:53 | history | edited | Deane Yang | CC BY-SA 3.0 |
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| Nov 3, 2013 at 12:08 | comment | added | Igor Belegradek | A classification is a list without redunancies. I think in this sense there is a classification of oriented compact 3-manifolds, which uses that (a) prime and JSJ decomposition is canonical. (b) lists of geeometric 3-manifolds (where for the hyperbolic case with toral boundary one has to quote the isomorphism problem for total relatively hyperbolic groups of Damani-Groves. See ldtopology.wordpress.com/2010/01/26/… for some detail. | |
| Nov 3, 2013 at 2:26 | comment | added | Autumn Kent | Technically there is a complete classification of 3-manifolds post-Perelman. In the Hyperbolic case, you know that the manifolds are determined by their fundamental groups (by Mostow Rigidity), and the isomorphism problem for torsion-free hyperbolic groups is solvable thanks to a theorem of Sela. | |
| Nov 3, 2013 at 2:15 | comment | added | Joseph O'Rourke | Thanks, Deane, your added note may highlight the core issue here. | |
| Nov 3, 2013 at 2:14 | history | edited | Deane Yang | CC BY-SA 3.0 |
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| Nov 3, 2013 at 2:04 | history | answered | Deane Yang | CC BY-SA 3.0 |