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Apr 6, 2010 at 7:29 vote accept Martin Brandenburg
Apr 6, 2010 at 1:16 comment added Ryan Budney I'd like to 2nd Church's opinion that proofs of the classification of surfaces can be very informative as the tools you use can be re-used in other circumstances. The key part of the proof is that surfaces can be triangulated (or given a polyhedral decomposition) and are turned into combinatorial objects where you can use homology to finish the classification. Morse theory or transversality (Sard's theorem) is an excellent approach to this if you're dealing with smooth surfaces. These are re-usable tools.
Apr 5, 2010 at 23:55 history answered Tom Church CC BY-SA 2.5