Mathematical Research Letters

Volume 2, Issue 3, May 1995 pp. 247-258.

Symplectic cuts

Authors: Eugene Lerman
Author institution: MIT

Summary: 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.

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