Normal-bundle obstruction to being a regular level set
= Normal-bundle obstruction to being a regular level set
If an embedded codimension-$k$ submanifold $X\subset M$ is $f^{-1}(y)$ for a <regular value> $y$ of a smooth map $f:M\to\mathbb R^k$, then $df$ identifies its <normal bundle> with the trivial bundle $X\times\mathbb R^k$. A submanifold with nontrivial normal bundle therefore cannot be such a regular level set. The core circle of the <Möbius band> is a codimension-one example.