Symplectic cuts

Abstract

According to McDuff the blow-up operation in symplectic ge- ometry amounts to a removal of an open symplectic ball followed by a col- lapse of some boundary directions. In this paper I describe a generalization of the blow-up constructionthe symplectic cut. In the case of symplec- tic 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.