Holomorphic triangle invariants and the topology of symplectic four-manifolds

Details Holomorphic triangle invariants and the topology of symplectic four-manifolds Holomorphic triangle invariants and the topology of symplectic four-manifolds

2002-01-08

arxiv.org/abs/math/0201049v1

Mathematics

Symplectic Geometry

35 pages, 2 figures

Scientific paper

This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in math.SG/0110169. Specifically, we establish a non-vanishing 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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