Are you aware of any short proofs for that fact (references)? And also for the fact that Morse cohomol. isomorphic to Singular cohomol.
Also, a silly question:
In the following thesis, he proves Morse cohomol$\cong$ sing. coho and then Morse cohomol$\cong$ De Rham coho (pg. 91). Doesn't it follow from De Rham's theorem that it is isomorphic to De Rham?
I am guessing he wanted to construct an explicit isomorphism. http://www.mat.univie.ac.at/~michor/schaetz_dipl.pdf
Thank you