Holomorphic triangle invariants and the topology of symplectic four-manifolds

Zolt�n Szab�, Peter Ozsv�th
2004 Duke mathematical journal  
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
more » ... ittings 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.
doi:10.1215/s0012-7094-04-12111-6 fatcat:54z2vpqlanb6zael2xm7k7zr5a