HIGHER BOTT-CHERN FORMS AND BEILINSONS REGULATOR

In this paper, we prove a Gauss-Bonnet theorem for the higher algebrai c K-theory of smooth complex algebraic varieties. To each exact n-cube of hermitian vector bundles, we associate a higher Bott-Chen form, ge neralizing the Bott-Chern forms associated to exact sequences. These f orms allow us to define characteristic classes from K-theory to absolu te Hedge cohomology. Then we prove that these characteristic classes a gree with Beilinson's regulator map.