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For any two connected n-dimensional topological manifolds one can construct the connected sum of them, but how did I know it is well defined? Thanks for any reference.

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Are you sure it's well-defined? You're not missing any words up there? –  user641 Jan 25 '12 at 5:29
Indeed, we need oriented here, IIRC –  Henno Brandsma Jan 25 '12 at 8:51
Lee proves this result in his book Introduction to Topological Manifolds. –  JSchlather Jan 25 '12 at 8:52
Yes. I negelect the oriented condition. But Lee's book only solve the surfaces case. –  MiGang Jan 26 '12 at 10:01
It's an exercise in Lee's Introduction to Smooth Manifolds. –  thomas j. Jan 26 '12 at 12:18

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