Families of Toeplitz operators, family index and deformation quantization
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909986679947264 |
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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 |