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15 January 2004 Holomorphic triangle invariants and the topology of symplectic four-manifolds
Peter Ozsváth, Zoltán Szabó
Duke Math. J. 121(1): 1-34 (15 January 2004). DOI: 10.1215/S0012-7094-04-12111-6

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.

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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

Information

Published: 15 January 2004
First available in Project Euclid: 21 December 2003

zbMATH: 1059.57018
MathSciNet: MR2031164
Digital Object Identifier: 10.1215/S0012-7094-04-12111-6

Subjects:
Primary: 57R
Secondary: 53D

Rights: Copyright © 2004 Duke University Press

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Vol.121 • No. 1 • 15 January 2004
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