Does anyone know a good book where I can find the computation of the de Rham Cohomology of surfaces in R^3 and other classical manifolds (higher dimensional spheres and projective spaces for example) ?
I found Tu's book "An Introduction Manifolds", where a computation is presented via Mayer-Vietoris sequences. However, it does not contain other examples. Does anyone know any other good material?
[Math] de Rham Cohomology of surfaces
at.algebraic-topologycohomology
Best Answer
For surfaces there's very nice and down-to-earth approach in Fulton's "Algebraic Topology" specially chapter 18 "Cohomology of Surfaces". For higher dimensional classical manifolds including the projective spaces see Karoubi's "Algebraic Topology via Differential Geometry" specially chapter V "Computing Cohomology". All of these use de Rham cohomology.