Timeline for Diffeomorphism of 3-manifolds
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2009 at 23:46 | comment | added | Paul Kirk | yes, if I'm recalling correctly: if there exist incompressible tori (or surfaces) then Waldhausen applies. Perelman says that atoroidal manifolds are either hyperbolic, so Mostow applies, or (simple) Seifert-fibered (and hence classified), I assume it is known precisely what non-Haken SF manifolds admit h.e. that aren't homotopic to diffeos, presumably just lens spaces. | |
| Dec 15, 2009 at 5:08 | comment | added | Tim Perutz | Thanks! Didn't know any of that. When you say "Perelman extends that", do you mean that, in light of Perelman, Waldhausen's arguments apply to all irreducible 3-manifolds with infinite $\pi_1$? | |
| Dec 15, 2009 at 4:23 | history | answered | Paul Kirk | CC BY-SA 2.5 |