Bohr-Sommerfeld quantization of $b$-symplectic toric manifolds

TL;DR

This paper introduces a Bohr-Sommerfeld quantization method for $b$-symplectic toric manifolds, linking it to geometric quantization and counting integral points in the moment polytope.

Contribution

It defines a new quantization approach for $b$-symplectic toric manifolds and proves its equivalence to existing geometric quantization methods.

Findings

Quantization dimension equals a signed count of integral points in the moment polytope.

The new quantization method coincides with the formal geometric quantization from prior work.

Provides a combinatorial interpretation of the quantization dimension.

Abstract

We define the Bohr-Sommerfeld quantization via $T$-modules for a $b$-symplectic toric manifold and show that it coincides with the formal geometric quantization of [GMW18b]. In particular, we prove that its dimension is given by a signed count of the integral points in the moment polytope of the toric action on the manifold.