Integrating a smooth family of differential forms

Asked Mar 19 '21 at 23:03

Active Mar 19 '21 at 23:03

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I have been trying to find a reference for the following :

Suppose I have a smooth family of differential forms $\omega_t$ that are exact. Then we can find a smooth family of differential forms $\mu_t$ such that $d\mu_t=\omega_t$.

I have been told this can be found in Bott and Tu's differential froms in algebraic topology but I could't find it anywhere . Does anyone know the specific chapter or another reference for this ?

Thanks in advance.

asked Mar 19 '21 at 23:03

Someone

4,737

Did you look at the Poincaré lemma? – Ted Shifrin Mar 20 '21 at 03:36
Yes I did . How does it help me ? @TedShifrin – Someone Mar 20 '21 at 08:07
Yes, of course you're right. The form on $M\times I$ will likely not be closed. You should look at the various posts referring to Moser's trick. – Ted Shifrin Mar 20 '21 at 17:38

Integrating a smooth family of differential forms

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