# Algebra/Topology Seminar

Algebra/Topology Seminar

Speaker: Nils Prigge (University of Cambridge)

Title: Tautological Rings of Fibrations

The tautological ring of smooth fibre bundles with fibre M is the subring of the cohomology of BDiff(M) generated by the generalised Miller-Morita-Mumford classes, which are defined as fibre integrals of characteristic classes of the vertical tangent bundle. I will discuss a generalization of this ring for fibrations which can be effectively studied using rational homotopy theory and gives an upper bound for the tautological ring for smooth fibre bundles. This will be particularly useful for some rationally elliptic manifolds, where this upper bound can be quite close.