Abstract
This article analyzes the interplay between symplectic geometry in dimension $4$ and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in [20]. 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 of four-manifolds along a certain class of three-manifolds obtained by plumbings of spheres. This leads to restrictions on the topology of Stein fillings of such three-manifolds.
Citation
Peter Ozsváth. Zoltán Szabó. "Holomorphic triangle invariants and the topology of symplectic four-manifolds." Duke Math. J. 121 (1) 1 - 34, 15 January 2004. https://doi.org/10.1215/S0012-7094-04-12111-6
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