Symplectic cuts

According to McDuff the blow-up operation in symplectic geometry amounts to a removal of an open symplectic ball followed by a collapse of some boundary directions. In this paper I describe a generalization of the blow-up construction–-the symplectic cut. In the case of symplectic manifolds with Hamiltonian circle action, the construction allows us to embed the reduced spaces in a symplectic manifold (“the symplectic cut”) as codimension 2 symplectic submanifolds. Several applications are discussed.