De Rham Theorem: Homotopy & Line Integrals Explained

[fisico30]

de Rham theorem...

hello Forum,

could someone explain in simple terms how the de Rham theorem relates to homotopy and line integrals in calculus, and conservative vector fields?

I know that if the curl of vector field is zero, then it isn't a conservative field necessarily...more conditions are needed (simple connectedness).

thanks!

 

[mathwonk]

read spivak's differential geometry, volume 1.