= Lefschetz coincidence number
{c}
{title2=$L(f,g)=\sum_i(-1)^i\operatorname{tr}(g^*f^!)$}
For maps $f,g:M\to N$ between closed connected oriented manifolds of equal dimension, the rational Lefschetz coincidence number is the displayed alternating trace, using the <cohomological pushforward between closed oriented manifolds>. Equivalently it evaluates the pullback by $(f,g)$ of the <cohomology class of the diagonal> on $[M]$. This formula fixes the signs with the product orientation on $N\times N$.
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