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RESEARCH BLOG 3/04/03 As noted in research blog 2/28/03, it appears that a main obstacle
 

Summary: RESEARCH BLOG 3/04/03
As noted in research blog 2/28/03, it appears that a main obstacle
in proving geometrization using Ricci flow is to show that one may
perform finitely many surgeries before the Ricci flow exists forever.
Perelman claims to have solved this in his paper [5]. I asked Perelman
by e-mail:
Hi,
I wanted to double check with you that you are claiming to
have a proof of the geometrization conjecture. Specifically,
you are claiming to have a proof that
1. You may do surgeries on horns so that there are only
finitely many in a given time interval
2. The volumes of horns are cTn
(for general n?) and this
shows that the Ricci flow will be non-singular after finitely
many of these surgeries.
thanks,
Ian Agol
1. is correct, 2. is correct with n replaced by 3/2 (the statement has
to be scale invariant, and n occured here by misprint), and only for

  

Source: Agol, Ian - Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

 

Collections: Mathematics