Spin-c Prequantization and Symplectic Cutting

TL;DR

This paper introduces spin-c prequantization for symplectic manifolds, explores the process of symplectic cutting in this context, and establishes conditions for its feasibility based on the moment map and prequantization choices.

Contribution

It defines spin-c prequantization for symplectic manifolds and characterizes the conditions under which symplectic cutting can be performed in this setting.

Findings

Spin-c prequantization combines a spin-c structure with a compatible connection.

Symplectic cutting in this context depends on the compatibility of the moment map level set with the prequantization.

The paper provides necessary and sufficient conditions for successful symplectic cutting with spin-c prequantization.

Abstract

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.