Ludovico Battista (Università di Bologna)

In dimension 3, combining the study of the geometry and the topology of manifolds led to interesting and surprising results. The generalization of such a connection in dimension 4 seems to be a promising approach to better understand this complicated world.
An intriguing 3-dimensional phenomenon is the existence of hyperbolic manifolds which fiber over the circle. Such manifolds cannot exist in dimension 4, due to a constraint given by Euler Characteristic and the Gauss - Bonnet formula. We will introduce the notion of "perfect circle-valued Morse function", which appears to be the natural generalization of "fibration over S^1", and we will introduce some tools to build a hyperbolic 4-manifold that admits such a function. To do this we will elaborate on a paper of Jankiewicz - Norin - Wise that makes use of Bestvina - Brady theory. Joint work with Bruno Martelli.