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This article analyzes the interplay between symplectic geometry in dimension 4 and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in  . Specifically, we establish a nonvanishing result for the invariants of symplectic four-manifolds, which leads to new proofs of the indecomposability theorem for symplectic four-manifolds and the symplectic Thom conjecture. As a new application, we generalize the indecomposability theorem to splittings ofdoi:10.1215/s0012-7094-04-12111-6 fatcat:54z2vpqlanb6zael2xm7k7zr5a