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Nov 19, 2011 at 15:01 comment added Tom Goodwillie Right. The statement makes sense without orientability, and the proof works, too, although there are surely many proofs that are easier to explain under the assumption of orientability. Besides, the general case follows from the orientable case by considering a two-sheeted covering space.
Nov 19, 2011 at 12:48 history asked marc CC BY-SA 3.0