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## Calculate the cohomology ring using Morse Theory [closed]

My question is: Is there any way to calculate the cohomology ring of a finite dimension manifold using the Morse theory?

The cohomology ring structure strongly rely on the following things $C^\ast(X\times Y)\cong C^\ast(X)\otimes C^\ast(Y)$. I cannot figure out how to use intersection to realize the ring structure.

This question originally come from the studying of Floer Homology and wonder there is a way of defining the cohomology ring of Floer homology just as finite dimensional.

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 Yes, see: mathoverflow.net/questions/101043/… – Chris Gerig Dec 25 at 16:25 @Chris Gerig: thank you for your help~ your question is really interesting – Siqi He Dec 25 at 16:33