Motivated by the goal of establishing a ‘symplectic sum formula’ in symplectic field theory, we will discuss the intersection behavior between punctured pseudoholomorphic curves and symplectic hypersurfaces in a symplectization. In particular we will show that the count of such intersections is always bounded from above by a finite, topologically determined quantity even though the curve, the target manifold, and the symplectic hypersurface in question are all non-compact.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
