Lecture 3. Submanifolds
... The Möbius strip is not orientable. I will not prove this rigorously yet.
Heuristically, the idea is that if we take an oriented pair of vectors at some
point (s, 0), and ‘slide’ them around the Möbius strip to (s + 1, 0), then if
there were an oriented atlas it would have to be the case that the ...