Characteristic classes of fiber bundles

Abstract

In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algberas of derivations. In fact, choosing a fiberwise metric, we construct a chain map to the de Rham complex on the base space, and show that the induced map on cohomology groups is independent of the choices. Moreover, we show that applying the construction to a surface bundle, our construction gives Morita-Mumford-Miller classes.