Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $f:M \to N$ is a smooth map between compact closed hypersurfaces $M$, $N \subset \mathbb{R}^n$, does it make sense to write the pushforward as $Df$, the total derivative? Because usually we require $M$ and $N$ to be open sets. If $f$ is a diffeomorphism, does the IFT hold true in the sense that I can write $(Df)^{-1} = Df^{-1}$?


share|cite|improve this question
This is common in many textbooks, for example Guillemin and Pollack's "Differential Topology". Yes, IFT holds. See the text. – Ryan Budney Dec 12 '12 at 0:03

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.