相关论文: On geometric quantization of $b$-symplectic manifo…

We consider a Hamiltonian action of n-dimensional torus, T^n, on a compact symplectic manifold (M,\omega) with d isolated fixed points. For every fixed point p there exists (though not unique) a class a_p in H^*_{T}(M; Q) such that the…

In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly we prove the orbifold versions of the abelian connectedness and convexity theorems. In the second half,…

Quantization of $R^2$ and $S^1 \times S^1$ phase spaces are explicitly carried out tweaking the techniques of geometric quantization. Crucial is a combined use of left and right invariant vector fields. Canonical bases, operators and their…

Let $M$ be a compact K\"ahler manifold equipped with a pre-quantum line bundle $L$. In [9], using $T$-symmetry, we constructed a polarization $\mathcal{P}_{\mathrm{mix}}$ on $M$, which generalizes real polarizations on toric manifolds. In…

We introduce the notion of regular symplectomorphism and graded regular symplectomorphism between singular phase spaces. Our main concern is to exhibit examples of unitary torus representations whose symplectic quotients cannot be graded…

When geometric quantization is applied to a manifold using a real polarization which is "nice enough", a result of Sniatycki says that the quantization can be found by counting certain objects, called Bohr-Sommerfeld leaves. Subsequently,…

We study the holomorphic symplectic structures on hyper-Kaehler manifolds of type A_{\infty}, by using the torus action.

We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical…

We introduce a pre-symplectic structure on the space of connections in a G-principal bundle over a four-manifold and a Hamiltonian action on it of the group of gauge transformations that are trivial on the boundary. The moment map is given…

We derive the quantization map in geometric quantization of symplectic manifolds via the Poisson sigma model. This gives a polarization-free (path integral) definition of quantization which pieces together most known quantization schemes.…

We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The…

We introduce a symplectic structure on the space of connections in a G-principal bundle over a four-manifold and the Hamiltonian action on it of the group of gauge transformations which are trivial on the boundary. The symplectic reduction…

These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…

We construct all possible Hamiltonian torus actions for which all the non-empty reduced spaces are two dimensional (and not single points) and the manifold is connected and compact, or, more generally, the moment map is proper as a map to a…

A symplectic toric orbifold is a compact connected orbifold $M$, a symplectic form $\omega$ on $M$, and an effective Hamiltonian action of a torus $T$ on $M$, where the dimension of $T$ is half the dimension of $M$. We prove that there is a…

To a complex symplectic manifold X we associate a canonical quantization algebroid. Our construction is similar to that of Polesello-Schapira's deformation-quantization algebroid, but the deformation parameter is no longer central. If X is…

Moduli spaces of polygons have been studied since the nineties for their topological and symplectic properties. Under generic assumptions, these are symplectic manifolds with natural global action-angle coordinates. This paper is concerned…

We show how to construct a resolution of symplectic orbifolds obtained as quotients of presymplectic manifolds with a torus action. As a corollary, this allows us to desingularise generic symplectic quotients. Given a manifold with a…

This paper examines the relationship between the symplectic quotient X//G of a Hamiltonian G-manifold X, and the associated symplectic quotient X//T, where T is a maximal torus, in the case in which X//G is a compact manifold or orbifold.…

We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact…