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Berezin Quantization and K-Homology

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Abstract

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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Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN 46202-3216, USA

    Erik Guentner

  2. Department of Mathematics, University of Hawai`i, M¯anoa, 2565, The Mall, Keller 401A, Honolulu, HI 96822, USA

    Erik Guentner

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  1. Erik Guentner
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Correspondence to Erik Guentner.

Additional information

Communicated by A. Connes

The author was supported by the NSF through an MSRI Postdoctoral Fellowship and other grants.

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Guentner, E. Berezin Quantization and K-Homology. Commun. Math. Phys. 240, 423–446 (2003). https://doi.org/10.1007/s00220-003-0913-6

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  • DOI: https://doi.org/10.1007/s00220-003-0913-6

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