Hi all!(adsbygoogle = window.adsbygoogle || []).push({});

I have a possibly trivial (possibly non-trivial? :rofl:) question. Here it is:

Assumption-Assume I have a closed p-form, whose integral over any p-cycle is always zero.

Statement-The closed p-form is also exact, by what is sometimes called de Rham's first theorem

My question is: what are the topological implications of my statement? (e.g. am I implying that all p-cycles are p-boundaries??)

Further question: de Rham's theorem is often proved for compact manifolds. Is my statement true even for manifolds which are not compact? (assume my manifold is paracompact, but not compact).

Thanks a lot!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# De Rham's first theorem

**Physics Forums | Science Articles, Homework Help, Discussion**