Differential characters as stacks and prequantization

TL;DR

This paper extends geometric prequantization from symplectic manifolds to differentiable stacks, establishing a bijection between principal circle bundles and second cohomology groups in an atlas-independent manner.

Contribution

It introduces a novel, stack-based framework for prequantization that generalizes classical methods to a broader geometric context.

Findings

Establishes a bijection between circle bundles and cohomology groups.

Provides an atlas-independent approach to prequantization.

Generalizes classical prequantization to differentiable stacks.

Abstract

We generalize geometric prequantization of symplectic manifolds to differentiable stacks. Our approach is atlas-independent and provides a bijection between isomorphism classes of principal circle bundles (with or without connections) and second cohomology groups of certain chain complexes.