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Peter Ozsváth and Zoltán Szabó developed Heegaard Floer homology, constructing invariants of three-manifolds from holomorphic-disk counts associated with Heegaard splittings. Their Berkeley lecture record explicitly identifies the joint discovery.^[ref]

Their four-manifold work uses pseudoholomorphic curves on triangular domains to define maps associated with cobordisms and assemble a smooth four-manifold invariant. The construction connects surface diagrams with information about smooth structures in four dimensions.^[ref]

Zoltán Szabó co-developed Heegaard Floer homology with Peter Ozsváth. The theory obtains invariants of a three-manifold by turning a Heegaard splitting into a Floer-theoretic chain complex.^[ref]

Their Holomorphic triangles and invariants for smooth four-manifolds by Peter Ozsváth and Zoltán Szabó extends the framework through Heegaard Floer cobordism maps. Compatibility under gluing lets data from pieces combine into an invariant of a closed smooth four-manifold, while blowup formulas describe its behavior under a controlled geometric modification.^[ref]