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Mar 1, 2012 at 9:00 comment added user18717 Your answer is quite encouraging!!!..I will start my learning journey!..
Mar 1, 2012 at 8:59 vote accept user18717
Feb 29, 2012 at 12:26 comment added Thomas Richard The book by Chow and Knopf is in my opinion the best available place to learn about Ricci Flow for itself, and its 3 sequels entitled "Ricci and its applications" are excellent references for any one working in the field. I should add two more references for Ricci flow for itself, there is the book by Chow, Lu and Ni "Hamilton's Ricci flow" which in my opinion is a bit harder than Chow and Knopf but covers a bit more material. There are also notes by P. Topping, available on his website, which goes up to the beginning of Perelman's work (F and W functionals) in a nice self-contained way.
Feb 29, 2012 at 9:59 comment added Deane Yang I also endorse Jonny's endorsement of the books written by Ben Chow with others (disclaimer: Ben and I have been friends since graduate school). I think Ben and his co-authors have gone to great pains to present the foundations of the Ricci flow very carefully and in great detail.
Feb 29, 2012 at 9:19 history edited Jonny Evans CC BY-SA 3.0
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Feb 29, 2012 at 9:09 history edited Jonny Evans CC BY-SA 3.0
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Feb 29, 2012 at 9:04 comment added Deane Yang As you say, Perelman's proof is completely different from Thurston-style topology. I am under the impression that you don't need to know much of the latter to understand Perelman's proof, which is all either analytic estimates or a careful geometric analysis of regions of the 3-manifold where the flow breaks down. It is useful to know at least a little bit of 3-manifold topology. In addition to Thurston's book, I recall a nice Bulletin of the AMS survey by Peter Scott.
Feb 29, 2012 at 8:13 history answered Jonny Evans CC BY-SA 3.0