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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 formal Szegö projections on the fibers. This allows us to define smooth families of Toeplitz operators. We apply these op…
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…
math.DG2022
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…