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Berezin Quantization and K-Homology
This paper appeared in the Communications in Math. Physics, 240
(2003), 423-446.
Abstract (from the preprint)
The E-theory defined by Connes and Higson provides a realization
of K-homology, the generalized homology theory dual to K-theory,
based on the notion of asymptotic homomorphisms. With this realization
it becomes possible to associate a K-homology element to a
quantization scheme. In this article we associate an asymptotic
homomorphism and K-homology element to the Berezin quantization of
a bounded symmetric domain. Further, we identify this element with
the element of K-homology defined by the Dolbeault operator of the domain.
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