Timeline for Diffeomorphism of 3-manifolds
Current License: CC BY-SA 2.5
3 events
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| Dec 15, 2009 at 21:59 | comment | added | Ryan Budney | The $\pi_1$ issue isn't really part of Mostow rigidity proper. Hyperbolic manifolds are $K(\pi,1)$'s so an isomorphism of the fundamental group is the same thing as a homotopy-equivalence of the spaces. The technique falls under basic obstruction theory, which in this case is pretty much "follow your nose". | |
| Dec 15, 2009 at 4:47 | comment | added | Tim Perutz | Right - indeed, MR is stronger still, in that it only requires an abstract isomorphism of $\pi_1$. The core of the question - I think! - is whether group theory, plus a bit of extra topological input, recognizes the geometric pieces of a 3-manifold. | |
| Dec 15, 2009 at 3:11 | history | answered | John Francis | CC BY-SA 2.5 |