Abstract: A surface bundle is a manifold that projects onto a base space with fibre over each point a surface.
The study of surface bundles over surfaces through numerical invariants has flourished since the sixties, after Chern, Hirzebruch and Serre proved a sufficient condition for the vanishing of their signature. In particular, Kotschick and others have studied the relations tying the signature to the Euler characteristic, and Kotschick, Hoster and Bucher have studied their simplicial volume.
I will present some new inequalites relating the simplicial volume of surface bundles to the two other invariants, improving known bounds on important families of such manifolds.
This is a joint work with Michelle Bucher.