Duke Mathematical Journal

Holomorphic triangle invariants and the topology of symplectic four-manifolds

Peter Ozsváth and Zoltán Szabó

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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 [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.

Article information

Duke Math. J., Volume 121, Number 1 (2004), 1-34.

First available in Project Euclid: 21 December 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R
Secondary: 53D


Ozsváth, Peter; Szabó, Zoltán. Holomorphic triangle invariants and the topology of symplectic four-manifolds. Duke Math. J. 121 (2004), no. 1, 1--34. doi:10.1215/S0012-7094-04-12111-6. https://projecteuclid.org/euclid.dmj/1072058748

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