From symplectic deformation to isotopy

Abstract

Let $X$ be an oriented 4-manifold which does not have simple SW-type, for example a blow-up of a rational or ruled surface. We show that any two cohomologous and deformation equivalent symplectic forms on $X$ are isotopic. This implies that blow-ups of these manifolds are unique, thus extending work of Biran. We also establish uniqueness of structure for certain fibered 4-manifolds.

Latex 16 pages. Revised version of Aug 4, 1997. The last section on symplectic fibrations has been improved

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