Zero Partition Cycles

Abstract

This thesis is concerned with characteristic classes of surface bundles. A complete description of the ring of stable rational characteristic classes is given by the work of Madsen and Weiss as the polynomial ring in the Miller-Morita-Mumford classes. This work introduces characteristic classes, which are are given by partitions of zeroes of abelian differentials. These classes are not new, but translate the notion of strata of abelian differentials to real-differential surface bundles. The Isomorphism-Theorem 4.4.3 exposes the partition classes as alternative basis for the ring of stable characteristic classes. The proof of the isomorphism theorem is carried out via a recursive computation in terms of the Miller-Morita-Mumford classes.