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Holomorphic triangle invariants and the topology of symplectic four-manifolds
| Venue: | Duke Math. J |
| Citations: | 46 - 5 self |
BibTeX
@ARTICLE{Ozsváth_holomorphictriangle,
author = {Peter Ozsváth and Zoltán Szabó},
title = {Holomorphic triangle invariants and the topology of symplectic four-manifolds},
journal = {Duke Math. J},
year = {},
pages = {2004}
}
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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.
