How do you use Meyer-vietoris sequence to compute the compact cohomology for Möbius strip without the bounding edge? Please give detail math. In particular explain how inclusion map is used.
On page 144 of here:
http://www.mat.univie.ac.at/~michor/dgbook.pdf
There is a proof. I do not understand the proof. I do not understand why the push forward inclusion map in cohomology should involve orientation at all. The definition of forms I thought is independent of orientation.