I'm reading "Mirror Symmetry" by Hori et al. In it, they compute the cohomology groups for the sphere and the torus. I tried to do the same for the Klein bottle, and it isn't working out.(adsbygoogle = window.adsbygoogle || []).push({});

Is Morse homology defined for non-orientable spaces? If not, why not? Can it be extended?

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# Morse-witten cohomology for non-orientable target spaces

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