blow-ups can also be performed in the symplectic category, by endowing the symplectic manifold with a compatible almost complex structure and proceeding with a complex blow-up. this makes sense on a purely topological level; however, endowing the blow-up with a symplectic form requires some care, because one cannot arbitrarily extend the symplectic form across the exceptional divisor "e". one must alter the symplectic form in a neighborhood of "e", or perform the blow-up by cutting out a neighborhood of "z" and collapsing the boundary in a well-defined way. this is best understood using the formalism of symplectic cutting, of which symplectic blow-up is a special case. symplectic cutting, together with the inverse operation of symplectic summation, is the symplectic analogue of deformation to the normal cone along a smooth divisor.