Dirac operator and Szegö projection define the same equivariant K-homology class on contact manifolds via deformation of principal symbols between calculi.
Bargmann,On a Hilbert space of analytic functions and an associated in- tegral transform, Comm
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Toeplitz Operators on Contact Manifolds and Equivariant K-homology
Dirac operator and Szegö projection define the same equivariant K-homology class on contact manifolds via deformation of principal symbols between calculi.