Bestvina–Brady Morse theory on hyperbolic manifolds

Inspired by the work of Jankiewicz, Norin, and Wise, in this thesis we describe that given a hyperbolic right-angled polytope, a colouring and a set of moves, it produces a hyperbolic manifold M with a map f: M→S¹. We apply this to a family of hyperbolic polytopes studied by Potyagailo and Vinberg, and by analyzing the resulting map we obtain a 5-manifold fibering over the circle, a 6-manifold with a perfect circle-valued Morse function, and a 7-manifold and a 8-manifold which fiber algebraically. These results are joint work with Giovanni Italiano and Bruno Martelli.