Geometric quantization on CR manifolds
Complex Variables
2020-11-04 v3 Differential Geometry
Abstract
Let be a compact connected orientable CR manifold with the action of a connected compact Lie group . Under natural pseudoconvexity assumptions we show that the CR Guillemin-Strernberg map is Fredholm at the level of Sobolev spaces of CR functions. As application we study this map for holomorphic line bundles which are positive near the inverse image of by the momentum map. We also show that "quantization commutes with reduction" for Sasakian manifolds.
Cite
@article{arxiv.1906.05627,
title = {Geometric quantization on CR manifolds},
author = {Chin-Yu Hsiao and Xiaonan Ma and George Marinescu},
journal= {arXiv preprint arXiv:1906.05627},
year = {2020}
}
Comments
52 pages; greatly revised version