Duke Mathematical Journal
- Duke Math. J.
- Volume 121, Number 1 (2004), 1-34.
Holomorphic triangle invariants and the topology of symplectic four-manifolds
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 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.
Duke Math. J. Volume 121, Number 1 (2004), 1-34.
First available in Project Euclid: 21 December 2003
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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. http://projecteuclid.org/euclid.dmj/1072058748.