= Graph intersection formula for mapping degree
{title2=$\deg(F|_{\partial D^m})=(D^m\times\{0\})\cdot\Gamma_F$}
For a smooth map of disk pairs whose <graph of a function> is transverse to the zero slice, orient the graph by its domain. With the tangent space of the zero slice ordered before that of the graph, the local <smooth intersection number> at a zero is $\operatorname{sgn}\det DF$. Summing these signs gives the relative <mapping degree> and hence the boundary <mapping degree>. Reversing the order of these two $m$-dimensional tangent spaces changes the sign by $(-1)^m$.
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