Let $f:\mathbb{R}^n\rightarrow \mathbb{R}$ be a (smooth) function and $a$ a regular value of $f$. Is there a (easy) way to determine the number of connected components of the submanifold $f^{-1}(a)$ ? One can assume extra regularity restrictions if necessary.
I am thinking about integration, cohomology or stuff like that. Any lead would be appreciated :)
Thanks