poincare conjecture

the math community has been abuzz, since they are getting closer to understanding grigori perelman’s (potential) solution to the poincare conjecture.  for those just tuning in, the poincare conjecture is generally understood as:

Every simply connected closed (i.e. compact and without boundary) 3-manifold is homeomorphic to a 3-sphere.
[wikipedia – whose page on the conjecture is superb]

that isn’t quite fair, though.  perelman appears to have proved the more fundamental conjecture (thurston) that every 3 manifold can be reduced to a simple geometry (eight possible).  from this, the poincare conjecture is a direct consequence.

i’m not going to re-hash all that has been written, since this is well outside basically everything i know about math.  but the MSM’s coverage feels like a bit of a tease.  since it seems that getting to the deeper stuff is something of a mess, here are the relevant links:

keep in mind, kleiner & lott’s “notes on perelman’s papers” (arxiv) is 192 pages long.


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