Families of Toeplitz operators, family index and deformation quantization
Differential Geometry
2026-01-13 v1 K-Theory and Homology
Symplectic Geometry
Abstract
Given a contact fibration, we construct smooth families of Szeg\"o projections on the fibers. This allows us to define smooth families of Toeplitz operators. We apply these operators to construct a deformation quantization of prequantizable symplectic fibrations, recovering a result of Kravchenko in an analytic way. We also derive a family index for these families of Toeplitz operators. To this end, we generalize an index formula of Baum and van Erp to families.
Keywords
Cite
@article{arxiv.2601.06619,
title = {Families of Toeplitz operators, family index and deformation quantization},
author = {Clément Cren and Erfan Rezaei},
journal= {arXiv preprint arXiv:2601.06619},
year = {2026}
}
Comments
34 pages, comments are welcome !