= Orientation criterion for a graph of symplectic planes
{title2=$\omega|_{\Gamma_A}=(1+\det A)\omega_D$}
Let $V=C\oplus D$ be a <symplectic orthogonal complement> splitting into two <symplectic subspaces> of dimension two. In <symplectic bases>, the <graph of a function> $A:D\to C$ pulls back the <symplectic form> to $\omega_D+A^*\omega_C=(1+\det A)\omega_D$. It is a <symplectic subspace> exactly when $\det A\ne-1$. Its <symplectic orientation> agrees with the orientation transported from $D$ exactly when $\det A>-1$. When $\det A<-1$, the transverse oriented pair $(C,\Gamma_A)$ has negative intersection sign, whereas two distinct complex lines in a compatible complex two-space have positive intersection sign.
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