On geometric quantization of $b$-symplectic manifolds

Abstract

We study a notion of pre-quantization for $b$-symplectic manifolds. We use it to construct a formal geometric quantization of $b$-symplectic manifolds equipped with Hamiltonian torus actions with nonzero modular weight. We show that these quantizations are finite dimensional $T$-modules.

8 pages

References in corpus (2)

• Applications of Equivariant Cohomology
• Convexity of the moment map image for torus actions on $b^m$-symplectic manifolds

Cited by in corpus (11)

• Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems
• Convexity of the moment map image for torus actions on $b^m$-symplectic manifolds
• Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
• Constructions of b-semitoric systems
• $b$-Structures on Lie groups and Poisson reduction
• A $b$-symplectic slice theorem
• Log symplectic manifolds and $[Q,R]=0$
• Geometric quantization of b-symplectic manifolds
• Bohr-Sommerfeld quantization of $b$-symplectic toric manifolds
• Integrable systems on singular symplectic manifolds: From local to global
• The Arnold conjecture for singular symplectic manifolds