Lin Weng, University of Kyushu, Fukuoka, Japan

Relative Bott-Chern secondary characteristic classes

Abstract

For smooth fibrations of compact Kaehler manifolds, the index theorem says that de Rham cohomology classes of the so-called index form is equal to the associated L²-form. However as differential forms, these two are very different. To measure their differences, we introduced relative Bott-Chern secondary characteristic classes. In this talk, we will explain our axiomatic approach to such classes, offer some details on their constructions and point out difficulties involved if time is allowed.