- #1
Silviu
- 624
- 11
Hello! I am reading this paper and on page 9 it defines the De Rham's period as ##\int_C \omega = <C,\omega>##, where C is a cycle and ##\omega## is a closed one form i.e. ##d\omega = 0##. The author says that ##<C,\omega>:\Omega^p(M) \times C_p(M) \to R##. I am a bit confused by this, as ##\omega## is an one-form so in order to give a real number it needs a vector, while here it receives a cycle, which I am not sure it is a vector. Does the author mean by this that you apply ##\omega## to the vector tangent at the cycle C on the manifold at each point and add up the values? Also he then uses this in association with Stokes theorem. However the ##\omega## appearing in the Stokes theorem is not necessary closed (##d\omega## is), so why can he still use the De Rham period there? Thank you!