 Gromov's compactness theorem (topology)

In the mathematical field of symplectic topology, Gromov's compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits to a pseudoholomorphic curve which may have nodes or (a finite tree of) "bubbles".A bubble is a holomorphic sphere which has a transverse intersection with the rest of the curve.