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]
https://math.berkeley.edu/about/upcoming-events/lecture-series/chern-lectures/2010-chern-lectures. Institutional account of joint discovery
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]
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