Related papers: On geometric quantization of $b$-symplectic manifo…

We study the formal geometric quantization of $b^m$-symplectic manifolds equipped with Hamiltonian actions of a torus $T$ with nonzero leading modular weight. The resulting virtual $T$-modules are finite dimensional when $m$ is odd, as in…

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…

We define formal geometric quantisation for proper Hamiltonian actions by possibly noncompact groups on possibly noncompact, prequantised symplectic manifolds, generalising work of Weitsman and Paradan. We study the functorial properties of…

In [GMPS] we proved that the moment map image of a $b$-symplectic toric manifold is a convex $b$-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on $b$-symplectic…

We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to…

We study Hamiltonian actions on $b$-symplectic manifolds with a focus on the effective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem that classifies these manifolds using polytopes that reside in…

We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The…

A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…

This thesis studies the pre-quantization of quasi-Hamiltonian group actions from a cohomological viewpoint. The compatibility of pre-quantization with symplectic reduction and the fusion product are established, and are used to understand…

We introduce a method of geometric quantization for compact $b$-symplectic manifolds in terms of the index of an Atiyah-Patodi-Singer (APS) boundary value problem. We show further that b-symplectic manifolds have canonical Spin-c structures…

The method of geometrical quantization of symplectic manifolds is applied to constructing infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(2)$. A formulation of the…

Let $M$ be a symplectic manifold, equipped with a Hamiltonian action of a torus $T$. We give an explicit formula for the rational cohomology ring of the symplectic quotient $M//T$ in terms of the cohomology ring of $M$ and fixed point data.…

Let G be an n-dimensional torus and $\tau$ a Hamiltonian action of G on a compact symplectic manifold, M. If M is pre-quantizable one can associate with $\tau$ a representation of G on a virtual vector space, Q(M), by…

Given a compact symplectic manifold $M$, with integral symplectic form, we prequantize a certain class of functions on the path space for $M$. The functions in question are induced by functions on $M$. We apply our construction to study the…

This text introduces geometric quantization on orbifolds. After reviewing the necessary background, it develops new treatments of prequantization, polarizations, and metaplectic correction for symplectic orbifolds.

The complex projective spaces, considered as prequantized symplectic manifolds, are roughly to the complete symmetric functions as those projective spaces, regarded as complex-oriented manifolds, are to Newton's power sums.

This paper determines a condition that is necessary and sufficient for a metaplectic-c prequantizable symplectic manifold with an effective Hamiltonian torus action to admit an equivariant metaplectic-c prequantization. The condition is…

The aim of this article is to study the functorial properties of the ``formal geometric quantization'' procedure which is defined for non-compact Hamiltonian manifolds (when the moment map is proper). For this purpose, we introduce a…

We study the geometric quantization process for twisted Poisson manifolds. First, we introduce the notion of Lichnerowicz-twisted Poisson cohomology for twisted Poisson manifolds and we use it in order to characterize their prequantization…

Let $G$ be a semisimple Lie group with finite component group, and let $K<G$ be a maximal compact subgroup. We obtain a quantisation commutes with reduction result for actions by $G$ on manifolds of the form $M = G\times_K N$, where $N$ is…