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Jan 14, 2011 at 11:13 vote accept ADL
Dec 24, 2010 at 18:52 comment added HJRW Well, Mark, both of these sets of ideas go into Sela's work. As you surely know, the train tracks that Bill mentions are, in a sense, dual to actions on R-trees. I wanted to make the point that our answers are not as different as they might superficially appear.
Dec 24, 2010 at 18:12 comment added user6976 Sela's proof is founded on Rips's theory of groups acting on R-trees which, in turn, is founded on Makanin-Razborov theory of equations in free groups.
Dec 24, 2010 at 0:31 comment added HJRW Perhaps I should add that Sela's work is founded on the sort of ideas that Bill sketches in his answer.
Dec 24, 2010 at 0:29 history answered HJRW CC BY-SA 2.5