I was reading through Lee's Smooth Manifolds on the part regarding orientations and I was wondering if the connected sum preserves the orientability of manifolds. Intuitively it seems to be true, but I'm not sure how to make this rigorous. Is the connected sum of orientable manifolds necessarily orientable and why?
2026-04-02 22:13:06.1775167986
Connected sum of orientable manifolds
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