Symplectic blowup
= Symplectic blowup
{title2=$\widetilde M$}
A symplectic blowup at a point removes a small <symplectic ball> and collapses its Hopf-circle boundary fibers, replacing the center by an <exceptional divisor> $E\cong\mathbb{CP}^{n-1}$. The resulting form agrees with the original form away from the surgery region, and its integral over a projective line in $E$ records the blowup size. In real dimension four, $E\cong\mathbb{CP}^1$ and $E^2=-1$.