= Gromov compactness for spheres
{c}
For a compact <symplectic manifold>, smooth convergence of tame <almost complex structures> and a uniform area bound give a subsequence of <J-holomorphic spheres> converging, after reparametrization, to a finite tree of <J-holomorphic spheres>, with convergence smooth away from finitely many bubbling points. The total <homology class> and <symplectic area> are preserved. Constant components may be added for stability. In a spherical class which cannot split into two positive-area spherical classes, there is only one nonconstant component.
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