Anti-symplectic involution
= Anti-symplectic involution
{title2=$\sigma^2=I,\ \sigma^*\omega=-\omega$}
An anti-symplectic involution is an <anti-symplectic map> whose square is the identity. Its nonempty <fixed-point set> is a <Lagrangian submanifold>; the linear version has complementary $+1$ and $-1$ <Lagrangian subspaces>.