Displaying similar documents to “On the index theorem for symplectic orbifolds”

Fourier-like kernels in geometric quantization

K. Gawędzki

Similarity:

CONTENTSI. Introduction............................................................................................................................................... 5II. Preliminary notions................................................................................................................................ 7III. Geometric quantization.........................................................................................................................12   A. Elements of...

Liouville forms in a neighborhood of an isotropic embedding

Frank Loose (1997)

Annales de l'institut Fourier

Similarity:

A Liouville form on a symplectic manifold ( X , ω ) is by definition a potential β of the symplectic form - d β = ω . Its center M is given by β - 1 ( 0 ) . A normal form for certain Liouville forms in a neighborhood of its center is given.

Geometric quantization and no-go theorems

Viktor Ginzburg, Richard Montgomery (2000)

Banach Center Publications

Similarity:

A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist....

Star products and local line bundles

Richard Melrose (2004)

Annales de l’institut Fourier

Similarity:

The notion of a local line bundle on a manifold, classified by 2-cohomology with real coefficients, is introduced. The twisting of pseudodifferential operators by such a line bundle leads to an algebroid with elliptic elements with real-valued index, given by a twisted variant of the Atiyah-Singer index formula. Using ideas of Boutet de Monvel and Guillemin the corresponding twisted Toeplitz algebroid on any compact symplectic manifold is shown to yield the star...