Symplectic cuts

Eugene Lerman

doi:10.4310/MRL.1995.v2.n3.a2

Symplectic cuts

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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.

Original language	English (US)
Pages (from-to)	247-258
Number of pages	12
Journal	Mathematical Research Letters
Volume	2
Issue number	3
DOIs	https://doi.org/10.4310/MRL.1995.v2.n3.a2
State	Published - Jan 1 1995
Externally published	Yes

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10.4310/MRL.1995.v2.n3.a2

https://doi.org/10.4310/MRL.1995.v2.n3.a2

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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.",

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year = "1995",

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AB - 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.

U2 - 10.4310/MRL.1995.v2.n3.a2

DO - 10.4310/MRL.1995.v2.n3.a2

M3 - Article

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SP - 247

EP - 258

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

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