Spectral triples from bimodule connections and Chern connections

  • Edwin Beggs

    Swansea University, UK
  • Shahn Majid

    Queen Mary University of London, UK

Abstract

We give a geometrical construction of Connes spectral triples or noncommutative Dirac operators starting with a bimodule connection on the proposed spinor bundle. The theory is applied to the example of , and also applies to the standard -sphere and the -disk with the right classical limit and all properties holding except for now being a twisted isometry. We also describe a noncommutative Chern construction from holomorphic bundles which in the -sphere case provides the relevant bimodule connection.

Cite this article

Edwin Beggs, Shahn Majid, Spectral triples from bimodule connections and Chern connections. J. Noncommut. Geom. 11 (2017), no. 2, pp. 669–701

DOI 10.4171/JNCG/11-2-7