## Topology Seminar

Hyperbolic geometry has been a powerful tool in the study of manifold

topology. Beyond the classical theory of surfaces, Thurston showed

that the family of surface bundles over the circle is a rich source of

hyperbolic 3-manifolds. In dimension 4, the correct analogue is given

surface bundles over surfaces. In order for such a bundle to admit a

hyperbolic metric, it needs to satisfy some conditions, such as being

atoroidal and having zero signature. Surprisingly enough, the first

examples of atoroidal surface bundles over surfaces were constructed

only a few months ago by Kent-Leininger. In this talk I’ll explain why

these examples also have signature zero, meaning that they could admit

hyperbolic metrics. This is joint work in progress with J-F. Lafont

and N. Miller.