Mathematical Research Letters

Volume 2 (1995)

Number 3

Symplectic cuts

Pages: 247 – 258

DOI: http://dx.doi.org/10.4310/MRL.1995.v2.n3.a2

Author

Eugene Lerman (Massachusetts Institute of Technology)

Abstract

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.

Full Text (PDF format)