Subject: Re:proof of Poincare/Geometrization Conjecture?
Date: Tue, 19 Nov 2002 15:38:11 -0500
From: Zbigniew Fiedorowicz
To: dmd1@lehigh.edu
CC: Zbigniew Fiedorowicz
This is a response of mine to a post by Greg Kuperberg on sci.math.research:
Dear Greg,
My understanding of what he is claiming is that, while he can't yet
fully prove Hamilton's conjectures, he can prove enough of them to
get the geometrization conjecture.
Earlier in his introduction he writes:
In this paper we carry out some details of Hamilton program. The
more technically complicated arguments, related to the surgery, will
be discussed elsewhere. We have not been able to confirm Hamilton's hope that
the solution that exists for all time $t\to\infty$ necessarily has
bounded normalized curvature; still we are able to show that the
region where this does not hold is locally collapsed with
curvature bounded below; by our earlier (partly unpublished) work
this is enough for topological conclusions.
Moreover in his abstract he writes:
We also verify several assertions related to Richard Hamilton's program
for the proof of Thurston geometrization conjecture for closed three-manifolds,
and give a sketch of an eclectic proof of this conjecture, making use of
earlier results on collapsing with local lower curvature bound.
Perhaps he meant to use some other word than "eclectic", but if you take
him literally, then he is claiming the geometrization conjecture.
Zig Fiedorowicz
>This is a serious paper with some very interesting results, but the
>author does NOT claim to prove the Poincare conjecture. When he says a
>"sketch", he clearly explains in the last section that he doesn't know
>how to fill in the sketch. He reduces the Geometrization Conjecture to
>a series of other conjectures about Ricci flow. And Richard Hamilton
>himself may or may not have recognized these conjectures a long time ago.
>Regardless it is good to write them down as Perelman has done.
--