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math.DG2026
Families of Toeplitz operators, family index and deformation quantization
Clément Cren, Erfan Rezaei
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 operator…
math.DG2025
A transverse index theorem in the calculus of filtered manifolds
Clément Cren
We use filtrations of the tangent bundle of a manifold starting with an integrable subbundle to define transverse symbols to the corresponding foliation, define a condition of tran…
math.DG2024
Toeplitz algebras and the Heisenberg group
Clément Cren
We show an isomorphism between an algebra which is naturally constructed from the Toeplitz algebra generated by d-shifts, and an ideal of the C * -algebra of the (2d + 1)-dimension…