Surface bundles over surfaces: new inequalities between signature,   simplicial volume and Euler characteristic
  We present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface bundles, namely the ones that arise through a ramified covering. These are the main known examples of bundles with non-zero signature. 
Michelle Bucher, Caterina Campagnolo
math.GT