Families of Toeplitz operators, family index and deformation quantization

Fuente: arXiv
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Main Authors: Cren, Clément, Rezaei, Erfan
Format: Preprint
Published: 2026
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author Cren, Clément
Rezaei, Erfan
author_facet Cren, Clément
Rezaei, Erfan
contents Given a contact fibration, we construct smooth families of Szegö 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_06619
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Families of Toeplitz operators, family index and deformation quantization
Cren, Clément
Rezaei, Erfan
Differential Geometry
K-Theory and Homology
Symplectic Geometry
Given a contact fibration, we construct smooth families of Szegö 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.
title Families of Toeplitz operators, family index and deformation quantization
topic Differential Geometry
K-Theory and Homology
Symplectic Geometry
url https://arxiv.org/abs/2601.06619