Re: [FOM] Poincaré Conjecture joeshipman at
Tue Jan 15 18:10:07 EST 2008

Now that it has been proved it is Delta^0. Previously it had been known 
to be Pi^1; prior to Rubinstein's algorithm for recognizing the 
3-sphere it was known to be Pi^2 (for all triangulated 3-manifolds X 
together with a combinatorial reduction of Pi1(X) to the trivial group, 
there exists a simplicial homeomorphism of X with the standard 

-- JS

-----Original Message-----
From: Apostolos Syropoulos <asyropoulos at>

Provided that it makes sense to ask, does anyone have any idea where
in the arithmetical hierarchy would one put Poincaré's Conjecture? I
mean is it a \Pi_2 problem, a \Pi_3
problem or what?

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