Extendability Theorem for Intersection Numbers/Corollary

This article needs to be linked to other articles. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{MissingLinks}} from the code.

Corollary to Extendability Theorem for Intersection Numbers

Let $f: X \to Y$ be a smooth map of compact oriented manifolds having the same dimension.

Let $X = \partial W$, where $W$ is compact.

If there is a smooth map $g: W \to Y$ such that $g {\restriction_X} = f$, then:

$\map \deg f = 0$

where $\map \deg f$ denotes the degree of $f$.

Proof

Follows immediately from the Extendability Theorem for Intersection Numbers.

$\blacksquare$