Higher Bott Chern forms and Beilinson's regulator

Abstract

Let X be a smooth complex algebraic variety. In this paper, we associate, to each exact n-cube of hermitian vector bundles over X, a differential form, called higher Bott Chern form, which generalizes the Bott Chern forms associated to an exact sequence of hermitian vector bundles. With these forms we construct characteristic classes for higher K-theory and prove that these classes agree with Beilinson's regulator. Thus we obtain a description of Beilinson's regulator map in terms of hermitian vector bundles.