In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algebras 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 choice of metric. Moreover, we show that, applied to a surface bundle, our construction gives Morita–Miller–Mumford classes.
"Characteristic classes of fiber bundles." Algebr. Geom. Topol. 16 (5) 3029 - 3050, 2016. https://doi.org/10.2140/agt.2016.16.3029