Prequantization of the Moduli Space of Flat ${\rm PU}(p)$-Bundles with Prescribed Boundary Holonomies

TL;DR

This paper investigates the conditions under which the moduli space of flat PU(p)-bundles with specified boundary holonomies can be prequantized, using quasi-Hamiltonian methods to identify obstructions.

Contribution

It provides a computation of the prequantization obstruction for moduli spaces of flat PU(p)-bundles with boundary conditions, extending the understanding of geometric quantization in this context.

Findings

Identifies the specific obstruction to prequantization.

Applies quasi-Hamiltonian techniques to moduli spaces.

Focuses on cases where p is an odd prime.

Abstract

Using the framework of quasi-Hamiltonian actions, we compute the obstruction to prequantization for the moduli space of flat ${\rm PU}(p)$-bundles over a compact orientable surface with prescribed holonomies around boundary components, where $p>2$ is prime.