Quotient-sphere degree identity
= Quotient-sphere degree identity
{title2=$\deg\widetilde F=\deg(F|_{\partial D^m})$}
Collapsing the boundary identifies the top <relative homology> of a disk pair with the top <reduced homology> of its quotient <sphere>. Together with the boundary <connecting homomorphism>, this shows that the induced quotient map and the boundary map have the same <mapping degree>, using the corresponding orientations.