Abstract
This paper is concerned with two themes of symplectic topology. The first is the development of techniques to construct symplectic manifolds and, in particular, compact symplectic 4-manifolds. The second is the resolution of symplectic singularities and, in particular, the resolution of isolated singularities in symplectic 4-manifolds. On the first topic we prove a theorem which allows the gluing of two symplectic manifolds along a special class of hypersurfaces that we call o-compatible hypersurfaces. Let (X, og) be a symplectic 2n-manifold and M c X a hypersurface with a fixed point free S 1-action. M is called o2compatible if the orbits of the action lie in the null directions of og[u. An ~o-compatible hypersurface M has a canonical co-orientation. Hence, if M is a separating hypersurface, then M divides X into distinguished components X and X +. In dimension 4, our main gluing theorem is as follows.
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