Spin-c Prequantization and Symplectic Cutting

Details Spin-c Prequantization and Symplectic Cutting Spin-c Prequantization and Symplectic Cutting

2007-10-23

arxiv.org/abs/0710.4270v2

Mathematics

Differential Geometry

23 pages. A section on prequantizing CP^n was added

Scientific paper

We define spin-c prequantization of a symplectic manifold to be a spin-c structure and a connection which are compatible with the symplectic form. We describe the cutting of an S^1-equivariant spin-c prequantization. The cutting process involves a choice of a spin-c prequantization for the complex plane. We prove that the cutting is possible if and only if the moment map level set along which the cutting is done is compatible with this choice.

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