Gromov proposed, in section 3.4.4(D) of "Partial Differential Relations", a program for resolving the singularities of symplectic immersions with symplectic crossings via blowing up, in exact analogue with the well known complex analytic technique. The purpose of this note is to show that this program cannot work. We show that there are symplectically immersed surfaces in symplectic 4-manifolds which do not have a symplectically embedded proper transform in any blow up of the four manifold. In particular, there are double points of a symplectically immersed surface which cannot be resolved symplectically using blowing up. Z ‹‰ .
This paper has been published: Differential Geometry and its Applications 6 (1996) 101-107.
Contact: mccarthy@math.msu.edu
Last Revised 7/9/99