Hyperbolic manifolds, maps to the circle, and fibring

We will discuss the problem of finding hyperbolic manifolds fibring over the circle; and show a method to construct and analyse maps from particular hyperbolic manifolds to S^1, which relies on Bestvina-Brady Morse theory. 
This technique can be used to build and detect fibrations, algebraic fibrations, and Morse functions with minimal number of critical points, which are interesting in the even dimensional case. 
After an introduction to the problem, and presentation of the main results, we will use the remaining time to focus on some easy 3-dimensional examples, in order to explicitly show the construction at work.