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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?2012-01-25
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    Indeed, we need oriented here, IIRC2012-01-25
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    Lee proves this result in his book [Introduction to Topological Manifolds](http://www.math.washington.edu/~lee/Books/ITM/).2012-01-25
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    Yes. I negelect the oriented condition. But Lee's book only solve the surfaces case.2012-01-26
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    It's an exercise in Lee's _Introduction to Smooth Manifolds_.2012-01-26

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