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Jan 5, 2016 at 16:39 comment added Igor Rivin My guess is that he was aware of it of DM, and having seen the complex hyperbolic structure, made the connection, and it all came together. By the way, you should read Bavard-Ghys, as well...
Jan 5, 2016 at 14:36 comment added Selim G Dear Igor, could you be a bit more specific about the fact that Thurston was familiar with Deligne and Mostow's work when he first came up with the flat metric interpretation of Deligne-Mostow's orbifolds? Because obviously Thurston has been aware of their work at some point, but the interesting question is whether it influenced or inspired in some way his own work.
Jan 5, 2016 at 13:14 history answered Igor Rivin CC BY-SA 3.0