Example: mod 2 Cohomology of The Real Projective Space
Let X = Pn(R), the real projective space. We compute the singular cohomology of X with coefficients in R := Z2.
Knowing that the integer homology is given by:
We have Ext(R, R) = R, Ext(Z, R)= 0, so that the above exact sequences yield
- .
In fact the total cohomology ring structure is
- .
Read more about this topic: Universal Coefficient Theorem
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