Spectral triples from bimodule connections and Chern connections

摘要

We give a geometrical construction of Connes spectral triples or noncommutative Dirac operators D starting with a bimodule connection on the proposed spinor bundle. The theory is applied to the example of M-2(C), and also applies to the standard q-sphere and the q-disk with the right classical limit and all properties holding except for J now being a twisted isometry. We also describe a noncommutative Chern construction from holomorphic bundles which in the q-sphere case provides the relevant bimodule connection.